(8) Lesson 7.7 - Area and Perimeter of Similar Figures

1. Course 3, Lesson 7-7
1. Graph the similar triangles: triangle LKM with vertices L(0, 2),
N(3, 4), M(0, 4) and triangle N(3, 4), P(3, 8), K(−4, 8). Then write
a proportion comparing the rise to the run for each of the similar
slope triangles and find the numeric value.
2. What is the slope of the line graphed below?

2. Course 3, Lesson 7-7
ANSWERS
1.
or
2.

LM NP
MN PK
2
3
3
2


3. HOW can you determine congruence and
similarity?
Geometry
Course 3, Lesson 7-7

4. Course 3, Lesson 7-7 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
• Extension of 8.G.4
Understand that a two-dimensional figure is similar to another
if the second can be obtained from the first by a sequence of
rotations, reflections, translations, and dilations.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

5. To
• find the perimeters and areas of
similar figures
Course 3, Lesson 7-7
Geometry

6. Course 3, Lesson 7-7
Geometry
Perimeter
Words If figure B is similar to figure A by a scale
factor, then the perimeter of B is equal to
the perimeter of A times the scale factor.
Symbols perimeter of perimeter of
figure B figure A
Models
Area
Words If figure B is similar to figure A by a scale
factor, then the area of B is equal to the
area of A times the square of the scale
factor.
Symbols area of area of
figure B figure A
= • scale factor
= • (scale factor)2

7. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
1. Two rectangles are similar. One has a length of 6 inches and
a perimeter of 24 inches. The other has a length of 7 inches.
What is the perimeter of this rectangle?
The scale factor is . The perimeter of the original is 24 inches.
Multiply by the scale factor.
Simplify.
Divide out common factors.
4
1
x = 28
So, the perimeter of the new rectangle is 28 inches.

8. Answer
Need Another Example?
Two rectangles are similar. One has a length
of 10 inches and a perimeter of 36 inches.
The other rectangle has a length of 7.5 inches.
What is the perimeter of this rectangle?
27 in.

9. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. In a scale drawing, the
perimeter of the garden
is 64 inches. The actual
length of AB is 18 feet.
What is the perimeter of
the actual garden?
The actual length is proportional to the length in the drawing with
a ratio of . Find the scale factor.
Convert feet to inches and divide out units.
Substitute. Then simplify.
perimeter of garden = perimeter of drawing • scale factor
P = 64 • 9 or 576
Find the perimeter of the actual garden.
The perimeter of the actual garden is 576 inches or 48 feet.

10. Answer
Need Another Example?
A model of a billboard has a side length of 3 inches.
The corresponding side on the actual billboard is 4 feet
long. The model has a perimeter of 42 inches. What is
the perimeter of the actual billboard?
672 in. or 56 ft

11. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
3. The Eddingtons have a
5-foot by 8-foot porch on
the front of their house.
They are building a
similar porch on the
back with double the
dimensions. Find the
area of the back porch.
The scale factor is 2.
Multiply by the square of the scale factor.
Evaluate the power.x = 40(4) or 160
The area of the front porch is (5)(8) or 40 square feet.
The back porch will have an area of 160 square feet.
x = 40(2)2

12. Answer
Need Another Example?
The Coopers bought a 6-foot by 9-foot
rectangular rug. They would like to buy a
similar rug with double the dimensions.
What will be the area of the new rug?
216 ft2

13. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-7
Geometry

14. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-7
Geometry
Sample answers:
• If two figures are similar, their perimeters are related by
the scale factor.
• If two figures are similar, their areas are related by the
square of the scale factor.

15. Explain how previous lessons
involving similar figures helped
you with today’s material.
Course 3, Lesson 7-7
Ratios and Proportional RelationshipsFunctionsGeometry