AREA AND VOLUME OF SIMILAR SHAPES WORKSHEET

For each pair of similar figures, find the unknown area.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

In the given figure, the area of triangle BCD is 6.4 cm². Find the area  of

(a)  Triangle ACE

(b)  Quadrilateral ABDE

Solution

Problem 5 :

Find

(a)  The value of x

(b)  The area of triangle PQT is given quadrilateral QRST has the area 22 m²

Solution

Problem 6 :

What will happen to the volume of 

(a) a sphere if the radius is doubled

(b)  A cylinder if the radius and the height are increased by 50% ?            Solution

Problem 1 :

Triangle DEC has area 4.2 cm².

a) Find the area of triangle ABC.

b) Find the area of quadrilateral ABED.

Solution

Problem 2 :

If triangle ABC has area 15 cm²:

a) find the area of ΔCDE

b) find the area of PQED.

Solution

Problem 3 :

What will happen to the volume of:

a) a sphere if the radius is doubled

b) a sphere if the radius is increased by 20%

Solution

Problem 4 :

Triangle A is similar to Triangle B. If the scale factor of ΔA to ΔB is 4 to 5, what is the ratio of the perimeters of ΔA to ΔB? ____________ What is the ratio of the areas of ΔA to ΔB? __________________

Solution

Problem 5 :

Pyramid X is similar to Pyramid Y. If the scale factor of X:Y is 3:7, what is the ratio of the surface areas of X:Y? __________ What is the ratio of the volumes of X:Y? ____________

Solution

Problem 6 :

The ratio of the surface areas of two similar cones is 16:49. What is the scale factor between the similar cones? __________ What is the ratio of the volumes of the similar cones? __________

Solution

Problem 7 :

Two spheres have a scale factor of 1:3. The smaller sphere has a surface area of 16 ft². Find the surface area of the larger sphere.

Solution

Problem 8 :

Two rectangular prisms are similar and the ratio of their sides is 2:3. The surface area of the larger rectangular prism is 1944 cm². What is the surface area of the smaller rectangular prism?

Solution

Problem 9 :

The ratio of the sides of two similar cubes is 3:4. The smaller cube has a volume of 729 m³. What is the volume of the larger cube?

Solution

Problem 10 :

Pyramid X is similar to pyramid Y. The Surface area of pyramid X is 135 cm², and the surface area of pyramid Y is 240 cm². If the volume of pyramid X is 189 cm³, then what is the volume of pyramid Y?

Solution

Problem 1 :

The two rectangles given below are similar. Find the perimeter of the rectangle EFGH.

Solution

Problem 2 :

The two parallelograms shown below are similar. Find the perimeter of the parallelogram ABCD. 

Solution

Problem 3 :

The perimeters of two similar triangles is in the ratio 3 : 4. The sum of their areas is 75 cm². Find the area of each triangle

Solution

Problem 4 :

The areas of two similar triangles are 45 cm² and 80 cm². The sum of their perimeters is 35 cm. Find the perimeter of each triangle. 

Solution

Problem 5 :

Cube B is an enlargement of cube A.

(a) What is the scale factor of enlargement?

(b) How many times larger is the surface area of B than A?

(c) How many times larger is the volume of cube B than A?

Solution

Problem 6 :

The surface areas of two similar shapes are in the ratio 25 : 81. The length of the smaller shape is 30 cm. Work out the length of the larger shape

Solution

Problem 7 :

The volumes of two similar shapes are in the ratio 1000 : 27. The surface area of the larger shape is 250 cm² Work out the surface area of the smaller shape.

Solution

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