Practice 10-4 Perimeters and Areas of Similar Figures
For each pair of similar figures, find a) the ratio of the perimeters
and b) the ratio of the areas.
DNG page 445
Ratio of Perimeters= a : b
Ratio of Areas= a2 : b2
a) 5 : 3 ;
b) 25 : 9
a) 3 : 4 ;
b) 9 : 16
a) 4 : 5 ; b) 16 : 25
Find the similarity ratio of each pair of similar figures.
4. two regular hexagons with areas 8 in2 and 32 in2
8
1 = 1 : 2 or 𝟏
Similarity ratio =

𝟐
4
32
5. two squares with areas 81 cm2 and 25 cm2
Similarity ratio =
81
25
= 9 : 5 or
10
360
= 1 : 6 or
𝟗
𝟓
6. two triangles with areas 10 ft2 and 360 ft2
Similarity ratio =
𝟏
𝟔
7. two circles with areas 128π cm2 and 18π cm2
128
64
𝟖
Similarity ratio =

= 8 : 3 or
18
9
𝟑
Similarity ratio = ratio of perimeters
Similarity ratio =
ratio of areas
Similarity ratio =
A2 : A1
Practice 10-4 Perimeters and Areas of Similar Figures
DNG page 445
For each pair of similar figures, the area of the smaller figure is
given. Find the area of the larger figure.
Ratio of Areas= a2 : b2
A =?
A =?
A =?
12 
A

20 in 2 5 2
2
15 cm
A

84 cm2 7 cm2
2
 122 
A  20 2 
 5 
 152 
A  84 2 
 7 
A  115.2 in2
A  385.7 cm
8 in
A

18 in2 5 in2
2
 82 
A  18 2 
5 
2
A  46.08 in2
Practice 10-4
DNG page 445
Perimeters and Areas of Similar Figures
For each pair of similar figures, find the ratio of the perimeters.
2
P1 x1 A1 x1

;
 2
P2 x2 A2 x2
P1

P2
A1
A2
1
P1
4

P2
1
2
2
P1 2
 or 2 : 1
P2 1
1
P1
12

P2
27
P1
12

P2
27
P1 2
 or 2 : 3
P2 3
2
1
P1
50

P2
8
P1
25

P2
4
P1 5
 or 5 : 2
P2 2
Practice 10-4 Perimeters and Areas of Similar Figures
DNG page 445
14.The shorter sides of a rectangle are 6 ft. The shorter sides
of a similar rectangle are 9 ft. The area of the smaller
rectangle is 48 ft2. What is the area of the larger rectangle?
9 ft
6 ft
A 92
 2
48 6
 92 
A  48 2 
6 
A  108 ft 2
The area of the larger rectangle is 108 ft2.