11.3f Perimeter and Area of Similar ∆s
11.3 Perimeters and Areas of Similar Figures
If two polygons are similar with the ratio Thm 11.7
of corresponding sides a : b, then the ratio of their perimeters is a : b and the ratio of their 2 2
areas is a : b
a
b
I
II
Polygon I ~ Polygon II
Ex 1
ABCD ~ RSTU
B
C
18
A
D
a) What is the ratio of their perimeters?
b) What is the ratio of their areas?
S
10
T
R
U
11.3f Perimeter and Area of Similar ∆s
Bell Ringers – May 18
Find the area of the figure.
1.
2.
9
11
20
16
30
15
8
3.
5
4
11.3f Perimeter and Area of Similar ∆s
Ex 2
Ex 3
A rectangular tablecloth is 60 in. by 120 in. A rectangular placemat made from the same cloth is 12 in. by 24 in. and costs $5. Compare the areas and find a reasonable cost for the tablecloth.
A small flat screen TV is 24 inches wide and 18 inches long. A larger TV is similar to the smaller one. The area of the larger screen is 675 square inches. Find the width of the larger TV.
Ex 4
A store sells trampolines that are all regular hexagons. One trampoline has a side length of 4.5 ft. and an area of 52.6 ft2. Find the area of the trampoline whose perimeter is 67.5ft.
2
11.3f Perimeter and Area of Similar ∆s
Guided Practice
1. The perimeter of ∆ABC is 16 ft, and its area is 64 square ft. The perimieter of ∆DEF is 12 feet. Given that ∆ABC ~ ∆DEF, find the ratio of the area of ∆ABC to the area of ∆DEF. Then find the area of ∆DEF.
Ratio of perimeters
16 4
=
12 3
Ratio of Areas
42 = 16
32 9
16 = 64
9 x
9*64 = 16x
x = 48
2. The ratios of the areas of two regular decagons is 20 : 36. What is the ratio of their corresponding side lengths in simplest radical form?
20 : 36
4*5 : 36
2 5 : 6
3. Rectangles I and II are similar. The perimeter of Rectangle I is 66 inches. Rectangle II is 35 feet long and 20 feet wide. Show the steps you would use to find the ratio of the areas and then find the area of Rectangle I.
Homework
Pages 740–743 # 1–4, 6–8, 10–22, 27–33