Section 8 – 6Perimeters & Areas

of Similar Figures

Objective:To find the perimeters and areas of

similar figures

Theorem 8 – 6Perimeters & Areas of Similar

FiguresIf the similarity ratio of two similar figures is , then:

1) The ratio of their perimeter is

2) The ratio of their areas is

Example 1 Finding Ratios in Similar FiguresA) The trapezoids at the right are similar. The ratio of the

lengths of corresponding sides is , or .

1) Find the ratio of the smaller trapezoids perimeter to the larger trapezoids perimeter.

2) In the same order as above, find the ratio of the areas.

B) Two similar polygons have corresponding sides in the ratio 5:7.

1) Find the ratio of their perimeters.

2) Find the ratio of their areas.

C) The triangles below are similar. Find the ratio (larger to smaller) of their perimeters and of their areas.

1) Find the ratio of their perimeters.

2) Find the ratio of their areas.

Example 2 Finding Areas Using Similar Figures

A) The area of the smaller regular polygon is about 27.5 . Find the area of the larger regular pentagon.

B) The corresponding sides of two similar parallelograms are in the ratio 3:4. The area of the larger parallelogram is 96 . Find the area of the smaller parallelogram

C) The ratio of the lengths of the corresponding sides of two regular octagons is 8:3. The area of the larger octagon is 320 . Find the area of the smaller octagon.

Example 3 Real-World Connection

A) The similarity ratio of the dimensions of two similar pieces of window glass is 3:5. The smaller piece costs $2.50. What should be the cost of the larger piece?

B) Jack plants the same crop in two rectangular fields, each with side lengths in a ratio of 2 : 3. Each dimension of the larger field is 3.5 times the dimension of the smaller field. Seeding the smaller field costs $8. How much money does seeding the larger field cost?

Example 4 Finding Similarity& Perimeter Ratios

A) The areas of two similar triangles are 50 and 98 . What is the similarity ratio? What is the ratio of their perimeters?

B) The areas of two similar rectangles are 1875 and 135 . What is the ratio of their perimeters?

C) The areas of two similar pentagons are 32 and7. What is the ratio of their perimeters?

Homework: