6.10
The student will
a) Define pi ( π) as a ratio of the
circumference of a circle to its diameter
b) Solve practical problems involving
circumference and area of a circle, given the
diameter or radius
c) Solve practical problems involving area
and perimeter
d) Describe and determine the volume and
surface area of a rectangular prism
Brain Pop
Area of Polygons
Objective 6.10 is really in three sections. Here is an overview.
Sections A and B and pi (π) 3.14 (we do this after Winter Break)
area of circles A =πr²
circumference of circles C = πd
Section C (Before Winter Break)
Area of squares A= lw or A= s²
3 in
A= 3² or A= 3 x 3
= 9 square inches
because squares have congruent sides
3 in
Perimeter of squares P= 4s or P= S+S+S+S
P= 4(3) or 3+3+3+3 P= 12 in
7 in
Area of rectangles A= lw
2 in
7 in
Perimeter of rectangles p = 2l + 2w or P= S+S+S+S
Area of triangles A=½ bh or A=b•h÷2
h=3 in
P= 14+4= 18 in
A= .5•4•3 A= 6 inches squared
because triangles are ½ a square or rectangle
4 in
3 in
2 in
Section D (after Winter Break)
Volume of a rectangular prism
A = 14 square inches
2 in P= 2(7) + 2(2)
A= ½ • 4 •3
b=4 in
Perimeter of triangles P= s+s+s
A= 7 • 2
V = lwh
Surface Area of a rectangular prism S.A. = 2lw + 2lh + 2wh
P= 2 + 3 + 4 P= 9 inches
Pg _____
6.10c
Directions- MA and PA….multiply area and perimeter add.
1. Draw a picture of the situation to determine if it is area or
perimeter. Label the measurements. Write formulas and solve
Draw & Key Word
Formula and Work
Answer
Key wordsArea- cover, carpet, grass, mow, an area, paint, tile
Perimeter- fence, trim, border, enclose, hem, edge, around
8 in
Examples
SQUARE
A= S²
or A= lw
A= 8 ²
A= 64 in²
A=8• 8
A= 64 in²
P= 4s
or
P= 4(8)
P= 32 in
P= s+s+s+s
P= 8+8+8+8
P= 32 in
10 in
6 in
RECTANGLE
A=lw
A= 10 •6
A= 60 in²
P= 2l + 2w
P = 2(10) + 2(6) Or for perimeter just add all the sides
P= 20 + 12
P= 32 inches
TRIANGLE (remember that ½ is .5)
A=½ bh
A= .5•6•7
A= 15 in²
P= s+s+s
H=7 in
6.10c Vocabulary
------------------------FORMULAS------------------Area of squares A= lw or A= s² because squares have congruent sides
Perimeter of squares P= 4s or P= S+S+S+S
Area of rectangles A= lw
Perimeter of rectangles p = 2l + 2w or P=
Area of triangles A=½ bh or A=b•h÷2
b=6 in
pg____
Polygon –A polygon is a simple, closed, two-dimensional figure
formed by three or more sides.
Area – It is the product of the length and the width
(A = l  w). The area of a triangle is one half of the measure of the
base times the height:
Perimeter –The perimeter of a polygon is the
measure of the distance around the polygon.
Length(l) - The measurement of the extent of something along its
greatest dimension.
Width(w) - The measurement of the extent of something from side
to side.
Base(b) – Bases are the top and bottom faces of a threedimensional object.
Height(h) –The shortest distance from the base of a parallelogram
to its opposite side.
Perimeter of triangles P= s+s+s
because triangles are ½ a square or rectangle
6.10c Practice
pg
1.
6.10c Practice
Find the area of a 13cm x 9cm rectangle.
Draw & Key Word
2.
Formula and Work
Formula and Work
Table cloth covers 6ft x 4 ft table.
Draw & Key Word
2. Sew a trim on a table cloth that is 6 ft x 4 ft.
Draw & Key Word
Formula and Work
Answer
Answer
Answer
3. Paint a wall that is 10 ft x 8 ft.
Draw & Key Word
Formula and Work
Answer
Formula and Work
Answer
4. How much frosting for a triangular shaped cake that’s
base 5 inches and height is 2 inches
Draw & Key Word
Formula and Work
Answer
Find the area of a triangle with a 7 mm height
and a 8 mm base
Draw & Key Word
6.
Answer
Find the perimeter of a square with a 6 ft side
Draw & Key Word
5.
Formula and Work
Answer
Find the area of a square with a 5 inch side
Draw & Key Word
4.
Formula and Work
Find the perimeter of a 20m x 10m rectangle.
Draw & Key Word
3.
1.
pg-
Formula and Work
Answer
Find the perimeter of a triangle with the sides
1in, 2in, and 3 inch.
Draw & Key Word
Formula and Work
Answer
5. Sewing a ribbon around a triangle with a base of 8
inches and two sides each 7 inches.
Draw & Key Word
Formula and Work
Answer
You plan to push three tables together for a
party. For one table, the length is 8 ft and
its width is 4 ft. All three tables are the
same size. What is the total area once you
push all three tables together?
6.10c
pg
You will be asked to determine area with partial
information. Draw the figures as shown.
Label each square, then figure out the total length
and width for each side.
18 cm
8 ft
You can solve by
figuring one
table’s area
and then
multiplying
by three
4 ft
A=lw
A=8 x 4
A= 32 ft²
3
3
3
3
3
3 cm
3 cm
3
32 ft
3
3
32ft
21 ft
32 x 3= 96 ft²
8 ft
Or determine the
new length and
width and then
solve area
12 cm
4 ft
7
7
A= lw
A= 18 • 12
A= 216 cm²
7 ft
4 ft
4 ft
4 ft
A= lw
A= 12 x 8
A= 96 ft²
4
4
4
16 ft
A=lw
A=21•16
A= 336 ft²
1) Rectangle 3ft x 7ft
5)
Area ______________Perimeter______
Area ____________Perimeter________
2) Triangle 14 cm base and 20 cm height
6) Rectangle 5 yards x 7 yards
Area _____________Perimeter_______
Area ___________Perimeter___________
3) RectangleEach little square is
4 cm x 4cm
4 cm
4 cm
Square 4 cm side
7) Triangle 14 foot base and 15 foot height
Area _____________
Area ____________Perimeter__________
8) Triangle 4.2 inch base and 14 inch height
4) Triangle 5 inch base and 13 inch height
Area ____________Perimeter___________
Area ___________Perimeter_________
6.10c
Math Word
Problems
Area and Perimeter
of
3 and 4 sided Polygons
1. Samantha owns a ranch that covers 48 square
miles. She will plant wheat on all the land except for
16 square miles. Samantha will plant wheat on
__________ square miles of land.
Draw & Key Word
a. 64
b. 32
c. 4
d. 768
Formula and Work
Answer
2. A rectangle is 5 inches wide. The area of the
rectangle is 35 square inches. What is the
perimeter of the rectangle?
Draw & Key Word
Formula and Work
a. 24 inches
b. 40 inches
c. 30 inches
d. There is not enough information to know.
Answer
3. John’s bedroom is exactly 18 feet
by 21 feet. He wants to get carpeting
to cover the entire floor. How many
square yards of carpeting does he
need?
Draw & Key Word
a. 126
b. 378
c. 13
d. 42
Formula and Work
Answer
Key Word
Formula and Work
Answer
Draw & Key Word
Formula and Work
Answer
Draw & Key Word
Formula and Work
7. What is the area of triangle RST?
R
5 in
S
13 in
12 in
T
Answer
8. What is the area of the large rectangle shown if each small
square is 2 inches wide and 2 inches long?
• 10. Sam and Abby are covering their table
with newspaper before beginning an art
project. Their table is 48 inches by 60 inches.
How many square inches of newspaper will
they need?
Draw & Key Word
Formula and Work
Answer
• 11. The brown tiles that the kids of KFMS
walk on, border a hall that is 80 foot long on
each side (there are two sides). How many
feet of brown tile is that?
Draw & Key Word
Formula and Work
Answer
• 12. June is painting her front door red. Her
door is 8 ft by 3 ft. How any feet of paint will
she need to cover the door?
Draw & Key Word
Formula and Work
Answer
• 13. A picture measures 5 inches by 5 inches.
How much wood is needed to frame the
picture?
Draw & Key Word
Formula and Work
Answer
• What is the area of the triangle?
H-6 inches
B- 10 inches
Draw & Key Word
Formula and Work
Answer
15. I am covering a triangular shaped slice of pie with
whipped cream. How much whipped will cover the pie?
b= 4
inches
H=6
inches
Draw & Key Word
Formula and Work
Answer
House Makeover!
Use the figuring box to answer each question
Draw & Key Word
Formula and Work
Answer
When you are finished answering the questions,
you may decorate your house in your style!
Answer the questions,
then glue your answers on
the back of construction
paper.
Next decorate your house.
Finally, the outside fits
over the inside on the
front of your construction
paper.
Name_________________ 6.10 c
It is time make over your new house for your first party!
Date___________
1. The kitchen floor needs to be retiled before every one comes to check out your new place. How many square feet of tile will you need to
buy?
2. The living room needs new carpet before the company arrives. How much carpet will you need to buy?
3. You are planning to cover the front door with really cool party paper The door is 7 feet tall and 3 feet wide. How many square feet of
party paper will you need to cover the door?
4. You are going to make a bright tablecloth for your 3’ X 4’ table. How many square feet of material will you need to buy?
5. You decided to add fringe to the edge of the tablecloth mentioned in question 4. How many feet of fringe will you need to buy?
6. You are going to enclose the front porch with lights. The porch is a rectangle that is 30 feet long and 6 feet wide. How many feet of lights
will you need?
7. You need to cover the couch cushions with a blanket because your sloppy brother is coming to the party. What a mess he makes! Your
couch is six feet long and three feet wide. How much area does the blanket need to cover?
8. Your flower garden is 10 feet by 3 feet and you would like to put a really neat fence border around it. How many feet of fenced border will
you need to buy?
9. Next, the lawn needs to be mowed before everyone gets to your house. Your yard is 50’ X 70’. How many square feet will you have to
mow?
10. Finally, the last yard project is putting a fence up around your 50’ X 70’ yard to keep your brother’s three big messy dogs out of the street
6.10 a and b
Area and Circumference of Circles
http://www.brainpop.com/math/num
bersandoperations/pi/
http://www.brainpop.com/math/geo
metryandmeasurement/circles/
Pg
6.10 a and b Directions
6.10 a and b
1. DR your circle
If Radius given, double for diameter
If Diameter given, halve for radius
2.
D- 10
R-5
10 in
D- 10
R-5
Determine what is being asked for,
AREA or CIRCUMFERENCE
3.
Write the formula and take one step at a
time
Area
Circumference
A= π x r x r
C= π x d
A= πr²
A= 3.14 x 5²
A= 3.14 x 25
A= 328.5 in ²
C= πd
C= 3.14 x 10
C= 31.4 in
pg 62
approximation
An inexact result adequate for a given purpose
Ex5 in
vocabulary
ratio
A comparison of two numbers by division. Example:
The ratio 2 to 3 can be expressed as 2 out of 3, 2:3, or
2/3.
circumference
The distance around the outside of a circle (like
perimeter)
distance is a little over 3 times the diameter
pi
The ratio of the circumference of a circle to the
diameter of a circle; equal to the fraction 22/7; often
written as the approximation 3.14
radius
The distance from the center of the circle to any
point on the circle (half diameter)
diameter
The distance across a circle through the center
(double radius)
Pg
Practice Circumference
Practice Area
6.10 a and b
pg
6.10 d
Volume and Surface Area of a
Rectangular Prism
http://www.brainpop.com/math/geo
metryandmeasurement/volumeofpris
ms/
Pg ____ 6.10 d
height
width
Examples:
6.10 d
w=12 in
h= 2 in
length
l=8 in
Surface Area- (measured in square units)
SA=2lw+2lh+2wh
Write this first
l = 8 in.
w = 12 in.
h = 2 in.
SA = 2lw + 2lh + 2wh
SA = 2(8)(12) + 2(8)(2) + 2(12)(2)
SA = 2(96) + 2(16) + 2(24)
SA = 192 + 32 + 48
SA = 272 inches²
Volume (measured in cubic units)
V=lwh
Write this first
l = 8 in.
w = 12 in.
h = 2 in.
V=lwh
V=(8)(12)(2)
V=192 in³
pg.
Rectangular Prism
Volume and Surface area
Net - An arrangement of
two-dimensional figures that
can be folded to form a polyhedron
Rectangular prism - A solid figure that has two
parallel and congruent bases that are rectangles
(a box)
Volume - (fill) The number of cubic units needed
to fill the space occupied by a solid. Answer is
cubed.
V=lwh
Surface area - (cover) The sum of the areas of all
the surfaces (faces) of a three-dimensional figure .
Answer is squared.
SA=2lw+2lh+2wh
Pg____
6.10 d Practice
Determine the Surface Area for
each Rectangular Prism
6.10 d Practice
Determine the Volume for each
Rectangular Prism
12 in
12 in
5 in
5 in
4 in
4 in
3 in
3 in
5 in
5 in
7 in
7 in
3 in
4 in
10 in
pg______
3 in
4 in
10 in