Unit 7 Triangles and Area
•This unit begins to classify triangles.
•It addresses special right triangles and the
Pythagorean Theorem (again).
•This unit covers the area equations required
for quadrilaterals, and for circles.
•It also covers the area of any polygon using
an apothem.
•This unit differentiates between perimeter and
area similarity ratios, and concludes with
Geometric Probability.
Standards
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SPI’s taught in Unit 7:
SPI 3108.1.1 Give precise mathematical descriptions or definitions of geometric shapes in the plane and space.
SPI 3108.1.2 Determine areas of planar figures by decomposing them into simpler figures without a grid.
SPI 3108.4.3 Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals and other
polygons.
SPI 3108.4.6 Use various area of triangle formulas to solve contextual problems (e.g., Heron’s formula, the area formula for an equilateral
triangle and A = ½ ab sin C).
SPI 3108.4.7 Compute the area and/or perimeter of triangles, quadrilaterals and other polygons when one or more additional steps are
required (e.g. find missing dimensions given area or perimeter of the figure, using trigonometry).
SPI 3108.4.11 Use basic theorems about similar and congruent triangles to solve problems.
SPI 3108.4.12 Solve problems involving congruence, similarity, proportional reasoning and/or scale factor of two similar figures or solids.
SPI 3108.5.1 Use area to solve problems involving geometric probability (e.g. dartboard problem, shaded sector of a circle, shaded region
of a geometric figure).
CLE (Course Level Expectations) found in Unit 7:
CLE3108.2.3 Establish an ability to estimate, select appropriate units, evaluate accuracy of calculations and approximate error in
measurement in geometric settings.
CLE 3108.3.1 Use analytic geometry tools to explore geometric problems involving parallel and perpendicular lines, circles, and special
points of polygons.
CLE 3108.4.6 Generate formulas for perimeter, area, and volume, including their use, dimensional analysis, and applications.
CLE 3108.4.8 Establish processes for determining congruence and similarity of figures, especially as related to scale factor, contextual
applications, and transformations.
CLE 3108.5.1 Analyze, interpret, employ and construct accurate statistical graphs.
CLE 3108.5.2 Develop the basic principles of geometric probability.
Standards
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CFU (Checks for Understanding) applied to Unit 7:
3108.1.5 Use technology, hands-on activities, and manipulatives to develop the language and the concepts of geometry,
including specialized vocabulary (e.g. graphing calculators, interactive geometry software such as Geometer’s Sketchpad and
Cabri, algebra tiles, pattern blocks, tessellation tiles, MIRAs, mirrors, spinners, geoboards, conic section models, volume
demonstration kits, Polyhedrons, measurement tools, compasses, PentaBlocks, pentominoes, cubes, tangrams).
3108.4.9 Classify triangles, quadrilaterals, and polygons (regular, non-regular, convex and concave) using their properties.
3108.4.10 Identify and apply properties and relationships of special figures (e.g., isosceles and equilateral triangles, family of
quadrilaterals, polygons, and solids).
3108.4.11 Use the triangle inequality theorems (e.g., Exterior Angle Inequality Theorem, Hinge Theorem, SSS Inequality
Theorem, Triangle Inequality Theorem) to solve problems.
3108.4.12 Apply the Angle Sum Theorem for polygons to find interior and exterior angle measures given the number of sides,
to find the number of sides given angle measures, and to solve contextual problems.
3108.4.20 Prove key basic theorems in geometry (i.e., Pythagorean Theorem, the sum of the angles of a triangle is 180
degrees, characteristics of quadrilaterals, and the line joining the midpoints of two sides of a triangle is parallel to the third side
and half its length).
3108.4.28 Derive and use the formulas for the area and perimeter of a regular polygon. (A=1/2ap)
3108.4.43 Apply the Pythagorean Theorem and its converse to triangles to solve mathematical and contextual problems in twoor three-dimensional situations.
3108.4.44 Identify and use Pythagorean triples in right triangles to find lengths of an unknown side in two- or three-dimensional
situations.
3108.4.45 Use the converse of the Pythagorean Theorem to classify a triangle by its angles (right, acute, or obtuse).
3108.4.46 Apply properties of 30° - 60° - 90° and 45° - 45° - 90° to determine side lengths of triangles.
3108.5.2 Translate from one representation of data to another (e.g., bar graph to pie graph, pie graph to bar graph, table to pie
graph, pie graph to chart) accurately using the area of a sector.
3108.5.3 Estimate or calculate simple geometric probabilities (e.g., number line, area model, using length, circles).
Pythagorean Theorem
• In a RIGHT triangle (a triangle with one
90 degree angle), the sum of the
squares of the lengths of the legs is
equal to the square of the length of the
hypotenuse (the longest side).
a
c
• a2 + b2 = c2
b
Pythagorean Triple
• A set of non-zero whole numbers a, b, and c that
satisfy the equation a2 + b2 = c2
• Some triples include:
• 3,4,5…5,12,13…8,15,17…7,24,25
• Recognize 3,4,5 and 5,12,13 they are the most
commonly used triples on standardized tests!
• If you multiply each number in a Pythagorean
triple by the same whole number, the 3 numbers
that result also form a Pythagorean triple.
• For example 3,4,5 x the whole number 2 equals
6 (3 x 2), 8 (4 x 2), and 10 (5 x 2), a new triple
Converse of the Pythagorean
Theorem
• If the square of the length of one side of
a triangle is equal to the sum of the
squares of the lengths of the other 2
sides, then the triangle is a right
triangle.
• In other words, if you calculate a2 + b2
and it does in fact = c2, then in fact you
can conclude that it is a right triangle
Proofs of the Pythagorean Theorem
• The Bride’s Chair
• The area of a square is Side x Side (or side
squared)
• Here, the side is a + b. So the area of the
square is (a+b)2
• The area of a triangle is ½ b x h
• This makes sense because the area of a
rectangle is base times height, so the area of
a triangle would be half of that
• Continuing on then, the area of the triangle in
the square then is ½ a x b
• There are 4 of these triangles, so the area
would be 4 x ½ x a x b
• Adding the area of the center square (c2), we
get (a+b)2 = 2ab + c2, which simplifies to
a2 + b2 = c2
A Proof Discovered by a High
School Student
• There are easily over 400 proofs of the
Pythagorean Theorem
• This one was discovered by a high school
student (Jamie deLemos) in 1995.
• We will learn that the area of a trapezoid is the top base plus the
bottom base divided by 2 (in other words we average the bases) x
the height.
• Here, that would be (2a + 2b)/2 x ab
• The area of a triangle is ½ b x h
• This would be 2a·b/2 + 2b·a/2 + 2·c²/2 for all of the triangles
• If you set them equal to each other, and reduce, you get a2 + b2 =
c2
• Remember, all of this is used to prove the LENGTHS of the sides,
not area
Area of a Triangle
• The area of a triangle is half the product
(multiply) of a base and the corresponding
height
• So, A = 1/2 x b x h
• The base of a triangle can be any of its sides.
The corresponding height is the length of the
altitude to the line containing that base.
• Right triangles are unique, in that you can
pick a base that automatically has a
corresponding height
h
b
Find the area of an Isosceles
Triangle
• Here, the height is not so easily seen as it is in a
right triangle. To find the height, we draw a line
perpendicularly from the base to the highest point
of the triangle
• To calculate the height, we can project a Right
Triangle, and determine the length of the 3rd side.
• 102+h2 = 122
12 m
• h2= 122-102
h
• h= 6.6
20 m
• Therefore, the area of this triangle is ½ x 6.6 x 20
• Or, area = 66 m2
Obtuse Triangles
• If the square of the length of the longest
side of a triangle is greater than the sum
of the squares of the length of the other
2 sides, the triangle is obtuse
• If C2>A2+B2 then the triangle is obtuse
A
B
C
Acute Triangles
• If the square of the length of the longest
side of a triangle is less than the sum of
the squares of the lengths of the other 2
sides, the triangle is acute.
• If C2<A2+B2 then the triangle is acute
B
A
C
Assignment
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Page 495-96 7-22,24-32
Page 497 36-42
Worksheet Practice 8-1
Worksheet 7-1
Unit 7 Quiz 1
Find the missing variable:
1. A = 6, B= 9, C = ?
2. A = 4, B = ? C = 11
3. A = ? B = 4, C = 13
4. A = 2, B = 13, C = ?
5. A =7, B = ? C = 14
6. D = 12, L = 18, H = ?
7. E = 11, D = 11, L = 20, H = ?
8. H = 14, D = 20, L = ?
9. L = 6, H = 4, D = ?
10.D = 22, L = 30, H = ?
A
C
B
D
E
H
L
Area of a Parallelogram
Height
• The area of a parallelogram is the base
times the height (b x h)
• Here is why 
• Remember the area of a rectangle is
base times height also
Basically you can
Base
cut a parallelogram
in half, and put the
two halves next to
each other to make
a rectangle
Perimeter
• The perimeter of a polygon is the sum
of the lengths of the sides –it is the
measure of how far around it is –like the
perimeter of your back yard, you would
measure how far around your back yard
it is.
Perimeter
• For any “regular” polygon, having
“n-sides”, the perimeter is n x the length
of one side (length = s)
• So a square would be 4s, a pentagon
would be 5s and so on
• Otherwise, just add the lengths of the
sides for a given irregular polygon
Area
• For simple polygons which have 90
degree angles –like squares and
rectangles, the area is equal to
side x side
• For a square, we write this: S x S –or S2
• For a rectangle we write this: L x W
S
W
S
L
Example
• What if you have
an irregular
shape like
below?
• Pick out different
shapes and add
them up
• 12 cm + 8 cm + 4
cm = 24 cm2
6 cm
2 cm
Area of a Trapezoid
• The area of a trapezoid is ½ times the
height times the top base (b1) + the
bottom base (b2)
• In other words, you average the top and
bottom (add them and divide by 2) and
multiply by the height
Area of a Trapezoid
• Here is how the area of a trapezoid
(1/2h(b1+b2) works: 
• Take a trapezoid, and make a mirror image
• Rotate the mirror image
• Now we have a parallelogram again, with the same height, but
the base is b1+b2 So the area of our new parallelogram is base
times height, or (b1+b2)xh. Since we only need one of them (we
only need 1 trapezoid, not 2), we use 1/2h(b1+b2)
B1
B2
B2
B1
B1+B2
Example
• To find the area of the trapezoid calculate
1/2h(b1+b2)
5m
• (b1+b2) = 5 + 7 = 12
• We don’t know the height
2√3
• We do have a 30/60/90 right
triangle.
600
7m
• We know the short side is 2 (7-5=2) 2
• So the long side (which is also the height)
is 2√3
• Therefore the area is ½(2 √3)(5+7) = 12 √3
• The area of a Rhombus or a Kite is ½ x
D1 x D2 (diagonal 1 and diagonal 2)
• Lets say D1 = 6 and D2= 6
• The area would be ½ x 6 x 6, or 18
• Imagine 1 triangle
• The area of this triangle is ½ x D1/2 x
D2/2
• This would be ½ x 6/2 x 6/2 or ½ x 3 x 3
= 4.5
• Since there are 4 triangles, we would
multiply 4 x 4.5 = 18
• The area of a kite can be proved
similarly
D1
Area of a Rhombus or a Kite
D2
Example
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Find the area of this kite
A = ½ x D1 x D2
A = ½ x (3+3) x (5+2)
A=½x6x7
A = ½ x 42
A = 21
2
3
3
5
Example
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15
12
Find the area of this Rhombus
9
A = ½ x D1 x D2
We know that D1 = 12 x 2 = 24
We need D2
We can either solve using the Pythagorean theorem,
or we can recognize the Pythagorean Triple (3,4,5)
So the third side of the triangle is 9 (3 x 3, 4 x 3, and
5 x 3)
Therefore D2 = 9 x 2 = 18
A = ½ x 24 x 18
A = 216
Assignment
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Page 619 8-16
Page 626 11-25
Worksheet 7-1
Worksheet 7-4
Unit 7 Quiz 2
1. What is the area equation for a triangle?
2. What is the area equation for a parallelogram?
3. What is the area equation for a rectangle?
4. What is the area equation for a square?
5. What is the area equation for a Trapezoid?
6. What is the area equation for a Kite?
7. What is the area equation for a Rhombus?
8. When C2>A2+B2 the triangle is _______
9. When C2=A2+B2 the triangle is _______
10. When C2<A2+B2 the triangle is _______
A look at the Circle
Diameter
Perimeter
.
Chord
Center Point
Radius
Circles
• A Circle is a set of points in a plane that are the same
distance from the center point
• A Radius is a segment of a line which has one
endpoint on the center point, and the other endpoint
on the circle
• A Diameter is a segment (or chord) that passes
through the center of the circle, and has an endpoint
on each side of the circle
• A Chord is any segment whose endpoints are on the
circle
• The Circumference is the distance around the circle.
• To calculate circumference, you multiply the Diameter
times pi, or 2 Radii times pi
Circumference
• Remember, circumference is the distance
around the circle
• The ratio of the circumference to the
diameter of the circle is represented as
• C=Dp or C = 2pR (1 diameter = 2 radii)
• This is called “Diameter Pi” or “2 Pi R”
 p is the symbol for “pi”, which is an often
used number  3.14159. Pi goes on
forever, but your calculator can give you a
good approximation
Find the Circumference
• A circle has a diameter of 10 feet. How
far around is it to the nearest tenth of a
foot?
• C = D x Pi
• C = 10 x 3.14
• C = 31.4 FT
10 Feet
Check on Learning
• Find the circumference for the following
circles:
• A circle with a diameter of 2 4/5 inches
– 8.79 inches
• A circle with a radius of 30 mm
– 188.495 mm
• A circle with a diameter of 200 miles
– 628.318 miles
• A circle with a radius of 14 feet
– 87.964 feet
Area of a Circle
• The area of a circle is calculated as:
 pR2
• This is called “pi R squared”
• Note: We can take the Diameter (D) and
divide it in two to get the Radius (R)
• We have to do this operation BEFORE
we square it
• So we could write this: p(D/2)2
More about π
• It’s been calculated for thousands of
years:
Culture/Person
Approximate Time
Value Used
Babylonians
2000 BC
3 + 1/8 = 3.125
Egyptians
2000 BC
3.16045
China
1200 BC
3
Bible mentions it
550 BC
3
Archimedes
250 BC
3.1418
Hon Han Shu
130
sqrt (10) = 3.1622
Ptolemy
150
3.14166
Bible Ref: He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and
five cubits high. It took a circumference of thirty cubits to measure around it.
More about π
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William Jones, a self-taught English mathematician born in Wales, is
the one who selected the Greek letter for the ratio of a circle's
circumference to its diameter in 1706.
is an irrational number. That means that it can not written as the ratio of
two integer numbers. For example, the ratio 22/7 is a popular one used
for but it is only an approximation which equals about 3.142857143...
Another more precise ratio is 355/113 which results in 3.14159292...
Another characteristic of as an irrational number is the fact that it takes
an infinite number of digits to give its exact value, i.e. you can never get
to the end of it.
Since 4,000 years ago and up until this very day, people have been
trying to get more and more accurate values for pi. Presently
supercomputers are used to find the value of with as many digits as
possible. Pi has been calculated with a precision containing more than
one billion digits, i.e., more that 1,000,000,000 digits!
More about π
• Egyptologists and followers of mysticism have been fascinated
for centuries by the fact that the Great Pyramid at Gaza seems
to approximate pi. The vertical height of the pyramid has the
same relationship to the perimeter of its base as the radius of a
circle as to its circumference.
• The first 144 digits of pi add up to 666 (which many scholars say
is “the mark of the Beast”). And 144 = (6+6) x (6+6).
• If the circumference of the earth were calculated using π
rounded to only the ninth decimal place, an error of no more
than one quarter of an inch in 25,000 miles would result.
• In 1995, Hiroyoki Gotu memorized 42,195 places of pi and is
considered the current pi champion. Some scholars speculate
that Japanese is better suited than other languages for
memorizing sequences of numbers.
Assignment
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Page 64 10-13, 23-33
Worksheet 1-7
Circles Worksheet
Discovering Pi
Unit 7 Quiz 3
A kite has a diagonal of 12 and a diagonal of 11. What is it’s area?
A rhombus has a diagonal of 2 and a diagonal of 8. What is it’s area?
A square has a side = 20 inches. What is it’s area?
A rectangle has a base of 16, and a height of 5. What is it’s area?
A parallelogram has a base of 8 and a height of 8. What is it’s area?
A triangle has a base of 18 and a height of 10. What is it’s area?
A triangle has a base of 11 and a height of 8. What is it’s area?
A trapezoid has a top base of 8, a bottom base of 9, and a height of 6.
what is it’s area?
9. A trapezoid has a top base of 4, a bottom base of 20, and a height of
23. What is it’s area?
10. A parallelogram has a base of 20 and a height of 23. What is it’s area?
1.
2.
3.
4.
5.
6.
7.
8.
Unit 7 Quiz 4 10 Points
• How do you calculate pi?
• Explain in your own words
Similarity
• Polygons are similar if they have the exact same
measure of degree for all angles, and that all
sides are proportional –they have the same ratio
• The similarity ratio is found by writing the length
of one side over the length of the same,
corresponding side from the second polygon
• For example, the similarity ratio here is 2/3 (3/4.5
= 2/3)
3
2
4.5
2 3
4
3
6
Perimeters and Area of
Similar Polygons
• If you have a similarity ratio between
two polygons  for example a/b, then:
• The similarity ratio for the perimeter is
the same  that is a/b
• The similarity ratio for the area is a little
different  it is a2/b2
• We can remember this because when
we label area it is always “squared” –for
example cm2
•
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Example
These polygons are similar
What is the similarity ratio?
6/9, which reduces to 2/3
If the perimeter of the small polygon is
20 m, what is the perimeter of the large
polygon?
2/3 = 20/P, 2P = 60, P = 30
If the area of the small polygon is 60 m2,
what is the area of the large polygon?
22/32 = 60/A, 4/9 = 60/A,
Cross multiply and divide: 4A = 60x9,
A = 135
6m
9m
Example
• The area of the small pentagon
is about 27.5 cm2
• What is the area, A, of the large
4 cm
pentagon?
10 cm
• 4/10 = 2/5
Notice, that you need to
2
2
• 2 /5 = 27.5/A
reduce the ratio (4/10 =
2/5) before you square
• 4/25 = 27.5/A
the top and bottom, or
• 4A = 25(27.5)
you will get the wrong
• 4A = 687.5
answer…
• A = 171.875 cm2
Find Similarity Ratios
• The area of two similar triangles are 50
cm2 and 98 cm2
• Find the similarity ratio A/B
• A2/B2 = 50/98 now simplify
• A2/B2 = 25/49 now square root all
• A/B = 5/7
• This is the similarity ratio, and the
perimeter ratio
Assignment
• Page 638 9-16,19-29
• Worksheet 8-6
Unit 7 Quiz 5 –All answers to
the nearest 10th
• A circle has a radius of 5.
1.
2.
What is it’s circumference?
What is it’s area?
• A circle has a radius of 8.
3.
4.
What is it’s circumference?
What is it’s area?
• A circle has a diameter of 12.
5.
6.
What is it’s circumference?
What is it’s area?
• A circle has a diameter of 30.
7.
8.
What is it’s circumference?
What is it’s area?
• A circle has a circumference of 12π
9. What is it’s diameter?
10. What is it’s area?
A Toss of a Coin
I inch Radius
• You are at a carnival, where they
have a coin toss
• They have an 8 inch square, with a
one inch radius circle on the square
• If you toss a quarter and the entire
quarter is on the circle, you win a
prize
• What is the probability of winning?
8 inches
The Solution
• A quarter is about 1 inch in diameter
• Therefore, to be completely on the 2
inch circle, the quarter has to be at
least ½ in from the edge of the circle
• This means the desired area is a
circle 1 inch in diameter (2 inch total,
minus ½ inch on each side, = 1 inch)
• The total area is the 8 inch square
• To calculate Probability, we
calculate the ratio of the desired
outcome divided by the total
outcome
• Therefore: π(.50)2/82 = .012 or 1.2%
• Not very good ODDS!!
8 inches
Probability
• The probability of an event occurring is the ratio
of the number of favorable outcomes to the
number of possible outcomes
• A geometric probability model is one in which
we use points to represent outcomes. (We will
also use area). You find probabilities by
comparing measurements of sets of points. For
example: if points of segments (like a number
line) represent possible outcomes, then 
• P(event) = length of favorable segment
length of entire segment
Example
• Suppose a fly lands on a 12 inch ruler’s
edge. What is the probability that the fly
lands on a point between 3 and 7?
P(landing between 3 and 7) =
1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12
4
12
Length of favorable segment = 4 or
Length of total segment
12
1
3
Another example
• A point on segment AB is selected at random.
What is the probability that it is a point found on
segment CD?
A
0
1
2
3
C
4
5
6
7
D
8
9
B
10
• How many favorable outcomes are there?
– Or, what is the length of the favorable segment?
– 4
• How many possible outcomes are there?
– Or, what is the length of the entire segment?
– 10
• P(point on CD) = length CD/length AB or 4/10 or
2/5
Bus example
• Elena’s bus runs every 25 minutes.
• If she arrives at her stop at a random
time, what is the probability that she will
have to wait at least 10 minutes for the
bus?
– Assume the stops take very little time
Bus Example
are 2 ways
solve this: the 25 minute wait
• There
Let segment
ABtorepresent
One
way isbuses.
the same as we did for the first problem:
between
10/25 = 2/5
• The
Let other
segment
AC represent any random wait,
way is this: The total possible
up to 10 minutes
before
probabilities
will add
up to the
one.bus arrives
– Therefore
arrives anywhere
Here,
we haveif 2Elena
probabilities
that must on
addsegment
up to
AC, she will have to wait at least 10 minutes
one.
– P(waiting
at the
least
10 min)
length
AC/length
The
first is 3/5,
other
is 2/5= for
a total
of 5/5 AB
– Or 15/25 or 3/5
– What is the probability that Elena will have to wait
less than 10 minutes?
A
0
5
10
C
15
?
20
B
25
Probability using regions or
Area
• If the points of a region represent
equally likely outcomes, then you can
find probabilities by comparing areas
• Where P(event) = area of favorable
region/ area of entire region
Target example
• Assume that a dart you throw will land
on a 1 foot square dartboard and is
equally likely to land at any point on the
board. Find the probability of hitting
each of the blue, yellow and red
regions. The radii of the concentric
circles are 1, 2 and 3 inches
respectively.
Target Example
•
•
Radii = 1 in (Blue) 2 in (Yellow) and 3 in (Red)
P(Dart in blue) = area of blue/total area
– = π(1)2/122
– which equals π/144 or .022, or 2.2%
•
P(Dart in yellow) = area of yellow/total area
– = (π(2)2 - π(12))/144
– Which equals 3π/144 or .065 or 6.5%
•
P(Dart in red) = area of red/total area
– = (π(3)2 - π(22))/144
– Which equals 5π/144 or .109 or 10.9%
•
•
12
12
What if the radius of the blue circle was doubled? What would the
probability be of hitting the blue circle? 4π/144 = 8.73%
What if it was tripled? What would be the probability of hitting the blue
circle? 9π/144 = 19.63%
Assignment
•
•
•
•
Page 671 8-16
Page 672 18-26
Bulls-eye Worksheet
Worksheet 9 Geometric Probability
problems
• Worksheet 7-8
• Geometric Probability quiz
Unit 7 Quiz 6 –All answers to
the nearest 10th
• A circle has a radius of 9.
1.
2.
What is it’s circumference?
What is it’s area?
• A circle has a radius of 11.
3.
4.
What is it’s circumference?
What is it’s area?
• A circle has a diameter of 13.
5.
6.
What is it’s circumference?
What is it’s area?
• A circle has a diameter of 40.
7.
8.
What is it’s circumference?
What is it’s area?
• A circle has a circumference of 14π
9. What is it’s diameter?
10. What is it’s area?
Unit 7 Quiz 7 2 points each
Round all answers to whole numbers
1. Find the area of a parallelogram with a base of 3 cm
and a height of 4 cm
2. Find the area of a trapezoid with a top base of 3 cm,
a bottom base of 5 cm, and a height of 5 cm
3. Find the area of a kite with a diagonal of 5 cm and a
second diagonal of 7 cm
4. Find the area of a circle with a radius of 5 meters
5. Find the circumference of a circle with a diameter of
10 inches
• Bonus for 2 points: Write the equation to calculate π
Unit 7 Quiz 7
Round to 2
decimal places
• Use the following information to
calculate the area of each slice of pie:
Car
Owner
1. Mustang
41%
2. Corvette
10%
3. Camaro
25%
4. G8
8%
5. BMW 5
5%
6. Jetta
7%
7. Viper
4%
Sports Car Owners
1
2
3
4
5
6
7
4%
5%
7%
41%
8%
25%
Radius: 10 in.
10%
To calculate a percentage of a total area, convert the percentage to a decimal, and
multiply times the area
Unit 7 Quiz 7 (10 points)
• Jason built a kid’s playhouse for his daughter
Amy.
• The playhouse is an exact replica of his
house.
• The playhouse has a perimeter that is five
times smaller than the real house (1:5 or 1/5)
• If the playhouse has an area of 100 square
feet, how many square feet is the real house?
At a minimum, show equation and solution
Unit 7 Final Extra Credit
Given: You randomly throw a dart, calculate the following:
• 2 points each:
1. What is the probability of not
hitting any circle, but instead
hitting the blue background
target?
2. What is the probability of
hitting any ring –red, yellow or
blue?
3. What is the probability of
hitting only the red ring?
4. What is the probability of
hitting only the yellow ring?
5. What is the probability of
hitting the blue circle?
12 inches
12 inches
The center circle has a
diameter of 4 inches and
each succeeding circle
has a 2 inch larger
diameter