Section 8-6 Perimeter and Area of Similar Figures SPI 22d: determine the perimeter & area given the ratio of 2 similar polygons Objectives: • find area and perimeter of similar figures
Section 8-6 Perimeter and Area of Similar Figures SPI 22d: determine the perimeter & area given the ratio of 2 similar polygons
Objectives:• find area and perimeter of similar figures
84
Similarity Ratio
Ratio of 2/3 a=2 and b=3
By the Theorem: Ratio of perimeter (small to large) is 2/3. Ratio of area (small to large) is 4/9.
Use the Similarity Ratio to Find Area and Perimeter
Find the perimeter and Area of the similar figures.
1. Find the similarity ratio:
2. Use theorem to find perimeter and area
Use the Similarity Ratio to Find Area and Perimeter
These two rhombi are similar. Their ratio of similarity is 3 : 1. Find x.
Set up Ratio Solve Proportion
3x = 12 x = 4
Finding Area using Similar Figures
The area of the small pentagon is about 27.5 cm sq. Find the area of the larger pentagon.
1. Find ratio of lengths of corresponding sides.
2. Write a proportion and solve. 4 = 27.525 A
4 = 210 5
The area is 22
52
= 4 25
4A = (25)(27.5) A = 171.875
Finding Similarity and Perimeter Ratios
The areas of two similar triangles are 50 cm2 and 98cm2. a. What is the similarity ratio?
b. What is the ratio of their perimeters?
1. Find the similarity ratio:
2. Simplify
= 25 49
The area is a2
b2
= 50 98
= 5 Take square root of both sides 7
ab
The similarity ratio of the fields is 3.5 : 1, so the ratio of the areas of the fields is (3.5)2 : (1)2, or 12.25 : 1.
Because seeding the smaller field costs $8, seeding 12.25 times as much land costs 12.25($8).
Seeding the larger field costs $98.
Benita plants the same crop in two rectangular
fields. Each dimension of the larger field is 3
times the dimension of the smaller field. Seeding
the smaller field costs $8. How much money does
seeding the larger field cost?
12
Real-world and Similarity Ratios