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Similar Shape Problems

In this worksheet, students solve problems involving similar shapes where the scale factor is known or can be found.

'Similar Shape Problems' worksheet

Key stage:  KS 2

Curriculum topic:  Ratio and Proportion

Curriculum subtopic:  Solve Shape Problems

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Similar shapes have matching corresponding angles and corresponding sides which are in the same ratio.

Similar triangles

In these two triangles, the angles match and you will notice that the second triangle has sides which are double the length of the sides of the first triangle.

The ratio of the bases is 3:6, which reduces like a fraction to 1:2.

The ratio of the heights is 7:14, which reduces like a fraction to 1:2.

 

 

Example

These two rectangles are similar.

Find the missing length.

Similar rectangles

 

Answer

The ratio of the bases is 4:8, which reduces to 1:2.

The big rectangle's sides are 2 times the matching sides of the small rectangle.

The missing side is 2 × 5 = 10 cm.

Look at these similar rectangles.

What is the ratio of their lengths, reduced to its lowest terms?

 

 Similar rectangles

5:10

1:2

3:6

10:5

Look at these similar rectangles.

What is the ratio of their lengths, reduced to its lowest terms?

 

 Similar rectangles

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar rectangles

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar rectangles

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar triangles

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar triangles

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar rectangles

These two shapes are similar.

What is the ratio of their lengths, reduced to its lowest terms?

 

 Similar shapes

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar triangles

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar shapes

  • Question 1

Look at these similar rectangles.

What is the ratio of their lengths, reduced to its lowest terms?

 

 Similar rectangles

CORRECT ANSWER
1:2
EDDIE SAYS
3:6 and 5:10 reduce like a fraction to 1:2.
  • Question 2

Look at these similar rectangles.

What is the ratio of their lengths, reduced to its lowest terms?

 

 Similar rectangles

CORRECT ANSWER
1:2
EDDIE SAYS
7:14 and 5:10 reduce like a fraction to 1:2.
  • Question 3

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar rectangles

CORRECT ANSWER
5
EDDIE SAYS
Ratio is 1:2, so missing length is half of 10.
  • Question 4

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar rectangles

CORRECT ANSWER
2
EDDIE SAYS
Ratio is 1:4, so missing length is a quarter of 8.
  • Question 5

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar triangles

CORRECT ANSWER
21
EDDIE SAYS
Ratio is 1:3, so missing length is 7 × 3 = 21.
  • Question 6

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar triangles

CORRECT ANSWER
3
EDDIE SAYS
Ratio is 1:5, so missing length is 15 ÷ 5 = 3.
  • Question 7

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar rectangles

CORRECT ANSWER
10
EDDIE SAYS
Ratio is 1:2, so missing length is double 5.
  • Question 8

These two shapes are similar.

What is the ratio of their lengths, reduced to its lowest terms?

 

 Similar shapes

CORRECT ANSWER
1:6
EDDIE SAYS
2:12 and 7:42 reduce to 1:6 like fractions.
  • Question 9

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar triangles

CORRECT ANSWER
25
EDDIE SAYS
Ratio is 1:5, so missing length is 5 × 5 = 25.
  • Question 10

These two shapes are similar.

State the missing length in cm.

(Just write the number.)

 

 Similar shapes

CORRECT ANSWER
21
EDDIE SAYS
Ratio is 1:3, so missing length is 3 × 7 = 21.
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