Transcript Chapter 8 Lesson 6

Chapter 8 Lesson 6
Objective: To find the perimeters
and areas of similar figures.
Theorem 8-6
Perimeters and Areas of Similar Figures
If the similarity ratio
a of two similar
figures is b , then
(1) the ratio ofatheir perimeters
is b and
2
a
(2) the ratio of their areas is 2 .
b
Example 1: Finding Ratios in Similar Figures
The trapezoids are similar. The ratio of the lengths
of corresponding sides is 6 or 2
9
3
1.Find the ratio (smaller to larger) of the
perimeters. 6 2
9
or
3
2.Find the ratio (smaller to larger) of the areas.
22 4

2
3
9
Example 2: Finding Ratios in Similar Figures
Two similar polygons have corresponding
sides in the ratio 5 : 7. Find the ratio of their
perimeters.
5
7
Example 3: Finding Ratios in Similar Figures
Two similar polygons have corresponding
sides in the ratio 5 : 7. Find the ratio of their
areas.
5
25

2
7
49
2
Example 4: Finding Areas Using
Similar Figures
The area of the smaller regular pentagon is about
27.5 cm2. Find the area A of the larger regular
pentagon.
All regular pentagons are similar.
Ratio of the lengths of the corresponding
2
sides is 4 or 2
2
4
10
5
or
The ratio of the areas is 52
25
172 cm2
Example 5: Finding Areas Using
Similar Figures
The corresponding sides of two similar
parallelograms are in the ratio ¾. The area of the
larger parallelogram is 96 in.2. Find the area of
the smaller parallelogram.
Area Ratio
3
9

2
4
16
2
9
x

16 96
16x  864
x  54
54in2
Example 6: Finding Similarity and Perimeter Ratios
The areas of two similar triangles are 50 cm2 and 98
cm2. What is the similarity ratio? What is the ratio of
their perimeters?
Find the similarity ratio a : b.
Example 7: Finding Similarity and Perimeter Ratios
The areas of two similar rectangles are 1875 ft2 and 135
ft2. Find the ratio of their perimeters.
a
1875

2
b
135
2
a
125

2
b
9
a
25 5

b
3
2
a 5 5

b
3
Assignment
Page 456
#1-8; 11-21; 26-31