SIMILAR SOLIDS WORKSHEET

The two polygons are similar. Find the value of x.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

Solution

Problem 8 :

Solution

Problem 9 :

Solution

Problem 10 :

Figure A has a perimeter of 60 inches and one of the side lengths is 5 inches. Figure B has a perimeter of 84 inches. Find the missing corresponding side length.

Solution

Problem 11 :

Figure A has an area of 4928 square feet and one of the side lengths is 88 feet. Figure B has an area of 77 square feet. Find the missing corresponding side length.

Solution

Problem 12 :

In the diagram triangle ABC ~ triangle ADE

a) Find the scale factor from triangle ABC to ADE

b) Find the value of x

c) Find <ABC

d) The perimeter of triangle ABC is about 42.4 units. Find the perimeter of triangle ADE.

e) The area of triangle ABC is about 71.75 square units. Find the area of triangle ADE

f) Is BC || DE explain your reasoning.

Solution

Problem 13 :

ABCDE ~ KLMNP 

a) Find the scale factor from ABCDE to KLMNP.

b) Find the scale factor from KLMNP to ABCDE.

c) Find the values of x, y, and z.

d) Find the perimeter of each polygon.

e) Find the ratio of the perimeters of ABCDE to KLMNP.

f) Find the ratio of the areas of ABCDE to KLMNP.

Solution

Find x given that the figures are similar :

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

A town plans to build a new swimming pool. An Olympic pool is rectangular with a length of 50 meters and a width of 25 meters. The new pool will be similar in shape to an Olympic pool but will have a length of 40 meters. Find the perimeters of an Olympic pool and the new pool

Solution

Problem 8 :

In the diagram, △ABC ∼ △DEF. Find the area of △DEF.

Solution

Problem 9 :

A school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. The school plans to make the width of the new court 45 feet. Find the perimeters of an NCAA court and of the new court in the school.

Solution

Problem 10 :

Describe and correct the error in finding the area of rectangle B. The rectangles are similar.

Solution

Problem 11 :

In the following the two polygons are similar. Find the values of x and y.

Solution

Problem 12 :

Solution

Problem 13 :

In table tennis, the table is a rectangle 9 feet long and 5 feet wide. A tennis court is a rectangle 78 feet long and 36 feet wide. Are the two surfaces similar? Explain. If so, find the scale factor of the tennis court to the table.

Solution

Consider the following similar shapes. Find

i) the scale factor

ii) the length or area marked by the unknown. 

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

Two similar triangles have a pair of corresponding sides of length 12 meters and 8 meters. The larger triangle has a perimeter of 48 meters and an area of 180 square meters. Find the perimeter and area of the smaller triangle.

Solution

Problem 8 :

You are making a scale model of a rectangular park for a school project. Your model has a length of 2 feet and a width of 1.4 feet. The actual park is 800 yards long. What are the perimeter and area of the actual park?

Solution

Problem 9 :

Figure A has an area of 48 square feet and one of the side lengths is 6 feet. Figure B has an area of 75 square feet. When the figures are similar, find the missing corresponding side length.

Solution

Problem 10 :

Figure A has an area of 18 square feet. Figure B has an area of 98 square feet and one of the side lengths is 14 feet. When the figures are similar, find the missing corresponding side length.

Solution

Problem 11 :

In the following exercises, JKLM ∼ EFGH.

a)  Find the scale factor of JKLM to EFGH.

b) Find the scale factor of EFGH to JKLM.

c) Find the values of x, y, and z.

Solution

Relates Pages

• Area of similar solids worksheet
• Volume of similar solids worksheet