Math Forum - Problem of the Week
Submissions for Funny Ducks
Student Short Answer Long Answer
Student 1
The area bounded by
the ducks is 615 sq ft
Student 2
The area of the walk
and pond that the
ducks use is 615 ft^2.
The Pond has an area of 17.5ft x 20.5 ft. Since the ducks stay exactly
3 feet from the pond on their walks, that means the corners are
rounded. Each corner is 1/4 of a circle with a radius of 3. The area
bounded by their path is: (17.5 x 20.5) + 2(17.5 x 3) + 2(20.5 x 3.5)
+ 3^2PI, 358.75ft^2 + 105ft^2 + 123ft^2 + 28.27ft^2 which equals
615.02ft^2 which rounds to 615ft^2
The area of the pond:
A=LxW
Ap = (20.5)(17.5)
Ap = 358.75 ft^2
________
__|__Aw___|__
|
| |
|
| |
As|
Ap | |20.5 ft
|
| |
__|________|_ |
|________|3ft
17.5 ft
As= The area of the path along the length= 3ft x 20.5ft = 61.5ft^2
Since there are two identical areas, one on each side of the pond
2As = 123ft^2
Aw= The area of the path along the width = 3ft x 17.5ft= 52.5 ft^2
2Aw = 105ft^2
The area of each corner is 1/4 of a circle.
Ac= The area of the 4 corners =( pi) r^2 = (pi)3^2= 28.27 ft^2
Total area is the sum of 2As +2Aw +Ac+Ap
358.75ft^2 + 123 ft^2 + 105 ft^2 + 28.27ft^2 =615.02 ft^2
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Page 1 of 13
Student 3
The area bound by the
path is 615 square feet
(including the pond's
area) or 256 square
feet (excluding the
pond's area).
20 feet6inches=20.5 feet
17 feet6inches=17.5 feet
The ducks walk at 3 feet from the pond all the time.This means that
the path is parallel to the pond's margins (at 3 feet distance) and
has the form of a quarter of a circle (with the radius of 3 feet) in
its corners.The area bound by the path (without the pond's area)is
made from 2 rectangles (20.5 feet * 3 feet), 2 rectangles (17.5 feet *
3 feet) and 4 quarters of a circle (with a 3 feet radius):
2*(20.5*3)+2*(17.5*3)+pi*3^2=123+105+28=256 square feet
(I rounded pi*9=3.14*9=28.26 to 28 square feet)
The total area bound by the path (including the pond's area) is:
256+20.5*17.5=256+358.75=614.75 square feet
Rounding the avove number we have 615 square feet.
Student 4
I found the answer for
the sidewalk's final
area to be 147 square
feet and the pond's
final area to be 523
square feet.
The answer is:
* the total area (including the pond's area) is 615 square feet
* the "ground" area (excluding the pond's area) is 256 square feet.
This POW is about a family of ducks that chose to live at a lily pond
25.5 feet long and 20.5 feet wide. Whenever they walked, they stayed
3 feet away from the pond. The problem is to find the area of the
sidewalk and pond.
My soliution for the area of the pond is 522.75 square feet, which
I rounded up to 523 square feet. I did it as the following:
20.5x25.5
For the solution of the sidewalk, I frist added 3 to each measurement
as follows:
(20.5+3)x(25.5+3)
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Page 2 of 13
Then I subtracted the area of the pond before rounding, in which I got
147 square feet. I got my answer by doing the following:
669.75-522.75
Student 5
Student 6
Student 7
My solution for the
area of the pathway is
1,476 feet and the
area of the pond and
pathway together is
5,781 feet.
the total area of the
pond and path is
615.05^ft.
The answer we got
was that the area of
the pond and the
sidewalk was 368 feet.
© 1994-2016 Drexel University
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I then checked my answer by redoing the entire problem. There is
really no way you can check this problem other than to check the
equations. I got the same answer every time.
Finally, I did not receive any help or had any influences on
finding the answer to this problem other than the teacher who told
everyone to do the problem. :oP
I did this by finding the area of ther pond and then the area of the
path and pond together. Then i subtracted the area od the pond from
the area of the path and pond together to find the area of the path
only. You can check this by making sure the path added to the pond
equals the total of the pond and path together.
first I found the lengths of the sides which were 17.5 and 20.5 ft
you had to add six ft to the length and width so the new lengths were
23.5 and 26.5. To find the area of those you have to multiply them
23.5 * 26.5 which equals 622.75^ft
next I have to find the area of the rounded corners. there are 4
rounded corners which equals one circle.the area for circles is A =
pi * r^. A = 3.14 * 3^. A = 28.3^ft.
the total area is 28.3 +622.75=651.05^ft.
then you have to subtract the square corners which is 36^ft.
651.05-36=615.05^ft
First we found the area of the pond. To find the area you multiply the
length by the width. The area of the pond is equal to 358.75 feet.
Then we added three inches to the length and the width. That would be
the area of the land between the duck path and the pond. Then we
found the area of both by multiplying new length, which was 20'9", and
by the width which is 17'9". The area we found was about 368 feet.
Then we figured that the total area minus the ponds area would give us
the area of the sidewalk. 368.3125'- 358.75'= 9.5625'. That is the
area of the sidewalk only. We then checked our answer by adding the
area of the pond with the area of the sidewalk to get the area of the
pond and the sidewalk. 358.75' + 9.5625'= 368.3125'.
Page 3 of 13
Student 8
The area of the entire
region is 615.02 feet
squared and the area
of the pathway is
256.27 feet squared.
Student 9
The area of the region
is 623 feet
Student 10
The area of the outside
path was 264ft2 while
the arae of the pnd
was 358.75 feet2 and
the total pond + Path
was 716.75 feet2
I found the area of the lilly pond which was 358.75. I then
found the area of the strips surrounding the lilly pond that the ducks
wlaked on: 52.5, 61.5, 52.5, and 61.5. I then knew that the corners
would have to be rounded for the ducks to stay exactly 3 feet from the
pond and that each corner was one quarter of a circle. The 4 corners
added up to one whole circle. The radius of the circle was 3 feet and
to find the area I multiplied 3.14 by 3 squared and came up with
28.27. I then added all of these numbers together and got 615.02. To
get the area of the pahtway you would add 52.5, 61.5, 52.5, 61.5, and
28.27 and you would come up with 256.27.
I can verify this because if you add 256.75 and 358.27 it equals
615.02.
I got this by adding six feet to the width and six feet to the length
of the pond since there is three extra feet on each end totaling
twelve. Then I multiplyed the numbers (23.5ftx26.5) to get 623 feet
see any changes at bottom of sheet. Done Chronologicaly.
first, i drew a diagram of both squares- the pond as one and the
dotted line
that they walked on as the 2nd one. Then i figured out the area of
the inside
pond by Multiplying 17.5 by 20.5
Then, i was confused about the numbers for the 2nd square, so i
counted the
squares from left the right and got two numbers- 23.5 and 26.5 ,
which I then
multiplyed toghter to get 622.75 ft2.
Okay, so now I have the inner and outer circle done, i just have to
find the
path, so i used my diagram again and SUBTRACTED the outer square, by
the inner
square.
This equation was 622.75 - 358.75 and anwser was 264 ft for the
path.
I confirmed my anwser by adding the path + the inner square to get
the outer
square , and by subtracting the path - outer square to get the inner
one.
This was helpful and confirmed my anwser.
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Page 4 of 13
Student 11
Student 12
Student 13
23 feet 6 inches long
and 20 feet 6 inches
widw with a total of 47
feet long and 41 feet
wide.
My solution is that the
path around the pond
is 264 ft. squared. The
total rectangle
including the path is
622.75 feet squared.
The area bounded by
the path of the ducks
to the nearest square
foot is 615 sq. ft.
© 1994-2016 Drexel University
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DOHH!!!
But i had frogot somthing though, they always stay 3 ft away form the
square, so when they turn corners, they go in a cricel, rather then a
square like form.
so, using the area for a circle, i did Pie Radius squared, and got
6.42. Then i found the total area of all the corners, which was (3 x
3 x 4= 36 ft), then subtracted that from the outer walkway (264 36) which equals 228, then i added the total circle area and Voila!
228 + 29.57 = 257.57 which is the area of the outer path!
So, for the total area, i would add 257.57 to the origial 266.75 and
for the total area got .. 524.34ft2!
The way I came to this answer is I added 3 feet to each side then double the two sides.
How I solved this problem was I figured out the demensions of the
lilly pond by multiplying the width by the length. Next I added 6 ft.
to both the length and the width. I did this because the ducks won't
walk any closer or farther than 3 ft. from the pond. From each point
on the pond it needs to go out three feet farther, this equalls six
feet total on each side. Now I multiplied the width by the length to
find the area. With this number I subtracted the area of just the pond
from the area of the total rectangle including the path. This told me
how large the path was. To verify my answer I added the pond's area
plus the sidewalk's area. This answer gives you the total of the large
rectangle.
Since the ducks always waddle 3 ft from the pond this path forms a
quadrilateral with rounded corners, since at the corner the duck stay
3 ft from a point which is part of a circle. So along the 20.5 ft
side 3 ft from it forms a 3 x 20.5 rectangle whose area is 61.5 sq.
ft. and you have two of them, one on each of the opposite sides. You
also have two 3 x 17.5 rectangles along the remaining opposite side,
these each have an area of 52.5 sq. ft. At each corner you have 1/4
of a circle with a radius of 3 ft, so all four corners form a circle
of radius 3 ft, using a value of pi=3.14 the area of this circle = pi
* 3^2 = 28.26 sq. ft. So the total area is 2* 61.5 + 2* 52.5 + 28.26
= 256.26 sq. ft. or approx. 256 sq. ft. Now add the area of the
pond, 17.5 x 20.5 = 358.75 sq. ft., 256.26+358.75 = 615.01 sq. ft. or
Page 5 of 13
about 615 sq. ft.
I will try to be more careful in the future
Student 14
The area of the entire
region bound by the
funny ducks path is
482 square feet.
Student 15
753 Square Feet.
Student 16
I got 615 square feet.
© 1994-2016 Drexel University
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Mike
L = length of pond = 20.5 feet.
W = width of pond = 17.5 feet.
L+3 feet = length of ducks path = 23.5 feet.
W+3 feet = width of ducks path = 20.5 feet.
Area of ducks path = (L+3)* (W+3)
= 23.5*20.5
= 481.75 square feet
= 482 square feet (rounded to nearest square foot)
Ok. First, I figured out what it would be without the 3 foot thing
around it. It was 27*17=459. Then, I figured out what it would be
on the 17 ft. ends if 3 ft. was added. It was 17*3=51 and doubled it
since there is 2 sides with 17 (102). Then I figured out the 26 ft.
sides. It was 26*3=78. Then I doubled that (156). Then I took
3*3=9 because of the corners and times that times 4 (36). Then I
added it all together. (459+102+156+36=753) And that is where my
answer came from.
I drew a picture to help me solve the problem this week. I drew a
rectangle for the pond and another bigger rectangle around it with
rounded corners to be the area where the ducks can walk. Then I drew
lines from the inside rectangle’s corners to the outer rectangle. Next
I labeled the distances – 20ft 6in for the length, 17ft 6in for the
width, and 3ft for distance between the two rectangles. I changed the
numbers into 20.5ft and 17.5ft. Then I multiplied those two numbers
and got 358.75ft squared. Next I did 20.5ft times 3ft and got 61.5ft
squared. Then I multiplied 61.5ft squared by 2 because there are two
of those rectangles. I got 123ft squared. Next I did 17.5ft times 3ft
and got 52.5ft squared. Then I multiplied 52.5 by two because there
are two of those rectangles. I got 105. To find a circle’s area you
have to multiply pie by radius squared. So I did 3ft (the radius)
squared which gave me 9ft and then 9ft multiplied by pie. That gave me
28.274ft squared. I did not have to divide by four to get a corner
because there are 4 corners, which makes one whole circle. Next I
added 123ft squared and 105ft squared and got 228ft squared. 228ft
squared plus 358.75ft squared is 586.75ft squared. Then I added 586.75
to 28.274ft squared to find the total area. That gave me 615.024ft
squared. I rounded it to the nearest square foot. I got 615 square
Page 6 of 13
Student 17
736 Sq. Ft.
Student 18
The area of the
rectangle is 623 square
feet.
Student 19
The total area
enclosed by the ducks'
walking is about 615
feet. (notice, if this is
not your answer, take
a look at the way I
approached this
problem. You will see a
difference)
Student 20
300 square feet.
Student 21
I got that the entire
region bound by the
path is 482 square feet
rounded to the nearest
square foot.
feet.
I added 3 twice to 17, and 3 twice to 26. Then I took 23 (17+6=23)
and 32 (26+6=32). 26*32=736.
Add 3 feet two times to each dimension because the ducks stay that
far away on both sides. So the dimensions of the rectangle are 20
feet 6 inches plus 3 feet plus 3 feet (or 26 feet 6 inches) and 17
feet 6 inches plus 3 feet plus 3 feet (or 23 feet 6 inches). The
area is then 26.5 feet times 23.5 feet or 622.75 square feet (rounded
to 623 square feet).
Solution is in web page, but here's the text:
To do this problem I first defined it. You'll notice the corners are
bent. This is because if I went straight out the ducks would be 3 *
sqr(2) feet away from the pool. So, I actually have four quarter
circles on the edges. Figuring this in my total area is:
Area = 20.5' * 17.5' + 2 * 3 * 17.5' + 2 * 3 * 20.5' + pie * (3²)'
A = 358.75' + 105' + 123' + 9 pie'
A = 586.75' + 9 pie'
A ~ 615 feet
Therefore, my answer is 615 feet
I figured this problem out by multipluing 26.5 by 17.5 and got 463.75.
Then I added 32.5+23.5=56, then I did 56/2=28. Then I squared the 28
to get 56 because we are required to give the answer squared. Then I
did pi*28squared and got 179.9. I then added 463.75 and 179.9 and got
639.65.
(I changed all inches to decimals)
What I did was I read the problem and saw the two measurements, 17ft.
and 6in. and 20ft. and 6in. Immeadiately, I realized that that 6
inches is the same as .5 because 6 is half of 12. Then I realized
that is said 3 feet away at all times. Therefore I added 3 to both
nubers and got 20.5 and 23.5. Then to get the area I multiplied them
together and got 481.75, and when it's rounded to the nearest square
foot, you get 482 square feet.
I am probably wrong so for the person who is reading this right now I
would like to tell you I am a guy, not a girl, and don't laugh at me
if my answer is wrong. Thank You for your cooperation!
© 1994-2016 Drexel University
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Page 7 of 13
Student 22
Student 23
Student 24
The area of the entire
region bound by the
path is 622.75 square
feet.
This area would be 623
square feet.
I belive that the area
bound to the duck's
path is 65 square ft.
What I did was actually quite simple: I added 6 ft to the length and
the width of the pond, thus giving me a similar rectangle exactly 3
ft bigger around on all the sides. Then I multiplied 26.5 ft X 23.5
ft to get my answer:622.75 square feet.
Since both the length and the width of the area bounded by the path
have to be 6 feet more than the length and width of the pond, we are
looking for an area of 26.5 ft * 23.5 ft = 622.75 sq. ft. This can be
rounded to 623 sq. ft.
The first step thet I took in solving my prrobleem was to convert the area of the pond in to innches. I took twenty feet
six inches long and came out with 246 inches. I then took seventeen feet six inches and converted that to come out
with 210 inches. I then drew a diagram of the pond. After this it said that the ducks always walked 3 feet away from the
edge of the pond. I then had to add 36 inches (three fett converted to inches) to each side. After this there were still
gaps in the corners. What I had tto do then was add 36 inches +36 inches to each corner. This is the equattion thaat I
used:
(246+288)+(36+36+36+36+36+36+36+36)=
(246+288)+(288)=
528+288=816
Student 25
The area of the region
bounded by the ducks'
path is 7257 square
feet.
Student 26
The area is 615.04
square foot.
I then had to convert the 816 inches in to feet. 816 divided by 12(inces in a foot) comes out to 68 square feet. So, my
finaal aswer is 68 square feet.
First I made a diagram of the pond itself and labeled the dimensions.
Then I added 3 feet to both dimensions and converted both
measurements into inches. Using the formula for the area of a
rectangle, I multiplied the length and the width together. Then I
divided that answer by 12 to convert it back into feet.
The area of the pool is 20.5 * 17.5 = 358.75 sq ft
The duck path is 3 ft from the pool, but when it turns angle, it forms a cicular path.
The circular part is like a quarter of a circle with radius = 3 ft.
Since there are 4 corners, the corner areas
= area of 1 circle with radius = 3 ft
= pi * 3**2
= 22 / 7 * 9
= 28.29 sq ft
The extra strips are 2 3ft strips along the width (17.5ft) and 2 3ft strips along the length (20.5ft)
= 2 * 3 * 17.5 + 2 * 3 * 20.5
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Page 8 of 13
= 228 sq ft
Student 27
The area of the region
bound by the path is
623 ft^2.
Student 28
The area of the region
bound by the path is
approximately 615
square feet.
Student 29
The total area bound
by the path that the
ducks waddle is 599
square feet.
So, total area
= area of pool + circle (corner pieces) + extra strips
= 358.75 + 28.29 + 228
= 615.04 sq ft
The original pond is 20.5 ft by 17.5 ft. The ducks walk 3 ft away
from the pond at all times, so the lenth of the path they walk is six
feet longer than the length of the pond(26.6 ft) and the width is six
feet wider than the width of the pond(23.5 ft). According to finding
the area of a rectangle(L*W), the area of the ducks path(rounded to
the nearest square foot) is 623 ft^2(26.6*23.5=622.75).
In solving this problem, I first considered the shape of the path. Since any given point on it would have a three foot
distance from the edge of the pool, the path would be rectanglish with quarter-circle corners with three-foot radii. So I
knew that the area would have to be the area of a rectangle with sides six feet longer than the pool's minus the four 9square-foot squares not included in the area, plus the area of a circle with a radius of three feet, since the four quartercircles added together would be equal to this. So I wrote the problem:
23.5*26.5 - 36 + 9¼ = 615 square feet (to the nearest foot)
The pond is 20 feet 6 inches long and 17 feet 6 inches wide.
To work out the area bound by the path that the ducks waddle, you must
work out the length and width of the path that they waddle.
The length of this path will be 20 feet 6 inches+3 feet+3 feet, as if
they stay exactly 3 feet from the pond at all times, there will be 3
feet added to either end of the length.
Therefore, the length of the path is 26 feet 3 inches.
The width of the path that the ducks waddle is based on the same logic
and thus is 17 feet 6 inches+3 feet+3 feet=23 feet 6 inches.
Student 30
The area of the pond
including the walkway
is 5781 square feet.
© 1994-2016 Drexel University
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To give the area of the path waddled by the ducks:
23 feet 6 inches*26 feet 6 inches=a
598 square feet 36 square inches=a
Rounding to give
599 square feet=a
First, I converted all my measurements to inches. I then added
three feet to both length and width. Once I got those two numbers, I
multiplied length by width to get the area. The area was 5781 square
feet.
Page 9 of 13
Student 31
My answer is the area
is 1,728 feet.
Student 32
The area of the entire
region bound by the
path in (the nearest
square foot)is 5217
square feet.
I got this answer by adding 3 feet to all lengths and widths.Then I
added both lengths together and both widths togehter. The total
lengths are 64 total feet. The total widths are 27 feet. Then i
multiplied 64 by 27 and my answer was 1,728 feet.
The I use to fine my anwer is to add 6 feet to 12 feet & 6 inches
because you add 3 on both ends of the 12 feet and 6 inches12+6=18 feet and 6 inches
The I add 6 feet to 17 feet & 6 inches for the same reason as above17+6=23 feet and 6 inches
I then convert all the feets into inches. therefore18*12 =216+6= 222
And 23*12 = 276+6= 282.
To find the Square feet of the region the ducks walked around. I
multiply 222 by 282:
222* 282= 62604 square inch.
Student 33
Student 34
Student 35
THe complete area of
the area of where the
ducks go is 486ft²
The complete area of
the described region is
622.75 square feet,
rounded to the nearest
square foot, would be
623 square feet.
Their path encloses
615 square feet. The
answer serves
mathematical intent
© 1994-2016 Drexel University
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I then divide 62604 by 12
62604/12 = 5217 square feet
That's how I found my answer.
I took the length of the pond and added the 3feet that they stayed
away from it and multiplied that by the 3feet added to the width
I am not quite sure that I arrived at the correct solution to this
problem because I may have overlooked a few details, as I
accidentally did the first time that I submitted a solution to this
website............. Here is my solution and how I got it:
I drew a rectangle enclosed by another rectangle and added 3 feet to
each side of each individual section of the rectangle, adding 6 ft.
to 20.5 ft (6 inches is 1/2 of a foot) to get 26.5 ft. I then added 6
ft to 17.5 ft. to get 23.5 ft. I multiplies 23.5 by 26.5 to get
622.75 square feet, which I rounded off to 623 square feet, my final
answer.
Notice that the path is a rectangle with rounded corners, which the
area can be arranged into the area of the pond+the area of the region
between the pond and their path during straight walking+the area of 4
quartercircles of radius 3 feet, very geometric.
Page 10 of 13
which the solution will
clarify.
Student 36
Student 37
The answer I got for
Funny Ducks was that
the total area was
622.75ft sq and the
area of the path was
264ft sq.
The area of the region
is 482 square feet.
Student 38
The area is 609'6".
Student 39
The area is 601 feet
That formula becomes lw+3(l+l)+3(w+w)+pi*3^2 or lw+6(l+w)+9pi.
Substituting l=20.5 feet and w=17.5 feet produces 615.024 square feet
for the area these funny ducks' path encloses.
How I did the problem was I first added 6ft to the length and width because the ducks stand three feet away from the
pond on both sides. So I multiplied26.5ft times 23.5ft and I got 622.75ft and that was the total area. Then I multiplied
20.5ft times 17.5ft to get the area of the pond and that was 358.75ft. Then I subtracted the total area from the area of
the pond to get the area of the path, which was 264ft. The way I checked the problem was I drew a diagram of the
pond and the path on graph paper to scale and then I counted the squares and got the same answer as before.
With the ducks always walking 3 feet from the pond, you must add 6
feet to each demension (3 feet per side). The demensions are then
26.5 feet and 23.5 feet. When you multiply them together you get an
answer of 481.75 which I rounded to 482.
First you would add six feet to the length and width of the pond to
account for the path that the ducks walk. Then you would take the
sum of the length and width and multiply it by twelve inches to make
everything inches.
20'+6'=26'times12"=312" then add the other 6" to get 318"
17'+6'=23'times12"=270" then add the other 6" to get 276"
Then you multiply 318" to 276" and you get 87768" squared.
Then you devide 87768" inches squared by 12" square inches
(144inches) and you get 609'6" squared.
So 609'6"is your answer.
I added 17 ft 6 in to 3ft which i got 20 ft. The i added another 3 ft
which i came up with 23 ft 6 in. Then i took 20'6 and added3' then
added another3' and came up with 26'6" . Then for the final step I
took 23'6" and timsed it by 20'6" and came up with the answer 601'
feet for the area. I wiil check my answer again
17.6
+ 6.o=23.6
20'6+ 6= 26.6
Student 40
My conclusion is that
the entire area used is
601 feet.
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23'6x26'6=601'
I came to my solution by drawing a picture of the pond with
measurements of 23'6" by 17'6". Then I added 3' to each side on all
four sides. I came up with the measurements 26'6' by 23'6". When I
multiplied those I first multiplied just the feet. 26 times 23 is
Page 11 of 13
598'. Then I added the inches to my solution of the feet. 6" times
6" is 36" which is the same as 3'. I added 3' to 598' and got a
total of 601'. My answer is 601' for the total area of the pond and
sidewalk path of the ducks.
17'6" + 3' + 3' = 23'6"
20'6" + 3' + 3' = 26'6"
26'*23'=598'
Student 41
588 square feet
Student 42
The total are of the
entire region bound by
the ducks path is
69,372 inches squared
or 5781 feet squared
The answer is 5781
square feet.
Student 43
Student 44
5781 square feet
Student 45
Area of path is 123 sq
feet. Area of path +
rectangle = 481.75 sq
feet.Area of rectangle
= 358.75 sq feet.
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6"*6"=36"
First, because I like working in inches better because there are no messy numbers, I converted everything to inches,
getting a pond 210x246 inches. I realized that the corners would be a problem, because if I simply added a 36x36 part
around it, at the corner it would be 36x((squareroot)(2)), not just 36. I concluded that each time the ducks walk around
a corner, they should instead walk a quarter circle with raduis 36, to keep them 36 inches away at all times. Becuase
there are 4 quarter circles, that makes exactly one circle, with an area of 36(pi). I added that to the area of the pond
(210*246), the extra included area that the ducks walked around on teh right and left (36*210*2), and the area like
that on the other two sides (36*246*2). I got 84605.09... for that answer. However, that is in inches, and I wanted
square feer, so I divided by 144 (12^2) to get feet, and ended up with 587.53..... Because the answer was supposed to
be to teh nearest foot, I rounded up to 588.
First I converted everything into inches to make the problem easier.
Next I added 36 inches (3 feet) to each side. Then I took the new
measurements (246 inches wide, 282 inches long) and multiplied them
together to get the area which came out to be 69,372 inches squared or
5781 feet squared.
Convert all feet into inches. Add 36 inches to all sides becuase of
the extra three feet. When you get that answer divide by 12 for feet
and you have your answer.
Basicall all you do is add 3 feet to 20ft 6in and 17ft 6in and you
should get 23ft 6in and 20ft 6in. Next you would convert them into
inches and you would get 246 and 282. Next multply them and get 69372
then divide by 12 and you would get the final answer as 5781 square
feet
Area of rectangle is length x width = 17.5 times 20.5 = 358.75 sq ft.
Area of new region is length + 3 x width + 3 = 20.5x23.5=481.75 sq ft.
Difference of 2 areas = area of path = 123 sq ft.
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Student 46
Student 47
Student 48
The area bound by the
bath in square feet is
166 feet and 9 inches.
My answer is 7473
square feet.
The area of the entire
region bound by the
path on which the
"Funny Ducks" walk is
69,372 sq. inches.
Since the width of the path is 3 feet, we must subtract 3 feet times 2
from each side. The sides are then 11 feet 6 inches and 14 feet 6
inches. Multiply them, and you get the area, 166 feet and 9 inches.
First of all, I converted all measerments to inches. Then, I added
72 inches to both sides and multiplied the two numbers. Then I
converted that number back to feet and got 7473 as the final answer.
First, I made a model and labeled it. Next, I added 3 feet to the
length and width (Separately). Then, I changed feet into inches to
make it easier and simpler to work with, then I calculated the area
of the region, using the number of inches for the length and width.
20'6" + 3'= 23'6"
17'6" + 3'= 20'6"
20ft. 6in = 246 in
23ft. 6in = 282 in
246 * 282= 69,372 sq inches
Student 49
It is approx. 615 ft^2.
Student 50
The complete area is
486 SQ FT.
ANSWER: 69,372 sq inches
First I made a diagram of the pond (20.5' x 17.5'). Then I added 3 ft. to all
sides. The rectangle now has rounded edges. So what I did was add the areas of each of the squares that I had to the
area of the cirlce that I now had. The large rectangle had an area of 358.75, the two smallest rectangles had areas of
52.5. And the middle sized rectangles had an area of 61.5. These added together are 472.5. There are 4 quarter
circles, thus this would be a circle 28.27433388... So you add this to 2 x 52.5 and 2 x 61.5 and 358.75. The answer is
615.0243339 which I rounded to the nearest, which is 615. This answer is ft. x ft. and that would be ft^2.
A=L*W
L=20.6+3.0
W=17.6+3.0
A=23.6*20.6
A=486.16=486 SQ FT
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