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Find the Area of Compound Shapes

In this worksheet, students will find the area of compound shapes, including circles.

'Find the Area of Compound Shapes' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation, Volume and Surface Area Calculations

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Alligator

Question

What do you call an alligator in a vest?

Answer

An investigator of course.

 

Lets investigate how to find the area of compound shapes including circles.

Compound shapes are shapes made up of two or more simple shapes.

All we need to know is the area of these simple shapes. Lets recap.

Boy looking thoughtful

Area of a square/rectangle/parallelogram = base x height

Area of a triangle = base x height ÷ 2  OR 1/2 base x height

Area of a circle = π x radius x radius (πr²)  

The value of Π is usually taken as 3.14 or use the Π button on your calculator.

 

Example 1

Area of compound shape

Here you can separate this shape into a rectangle measuring 9 cm x 8 cm = 72 cm² and a semi circle.

To find the semi circle find the area of the full circle π x 3 x 3 =  28.27 now divide by 2 =  14.14 cm²

Now just add 72 cm² to 14.14 cm² = 86.14 cm²

 

Example 2

Area of compound shape

Area of the triangle = 7 x 9 = 63 cm² ÷ 2 = 31.5 cm²

Area of the semi circle = π x 5 x 5 = 78.54 cm² ÷ 2 = 39.27 cm²

Total area = 31.5 cm² + 39.27 cm ² = 70.77 cm²

 

Your turn to investigate.

What is the area of this shape?

The the answer has been rounded to 2 decimal places (2 d.p)

25.14 cm²

171.27 cm²

75.41 cm²

146.14 cm²

Area of compound shape triangle and semi circle

Calculate the area of this shape.

Round your answer to 2 decimal places.

Write your answer in figures without the units.

 

 352.47 cm²261.62 cm²129.81 cm²
The area of this shape is

semi circle and a rectangle

Calculate the area of this shape.

Round your answer to 2 decimal places (2 d.p)

 352.47 cm²261.62 cm²129.81 cm²
The area of this shape is

triangle and semi circle

 100.45 cm²90 cm²245.96 cm²45 cm²190.48 cm²200.96 cm²100.48 cm²
The area of the triangle is
The area of the semi circle is
Total area is

compound area circle and square

Find the area of the shaded green part of the square.

Round your answer to 2 decimal places.

Write your answer in figures without the units.

 58 cm²108.24 cm²66.57 cm²102.65 cm²
The area of this shapes is

Semi circle and triangle

Find the area of this shape.

Round your answer to 2 decimal places.

Write your answer in figures without the units.

Find the area of the pink shaded triangle.

110.42 cm²

78.54 cm²

122.54 cm²

34.54 cm²

Find the area of the orange shape.

110.42 cm²

78.54 cm²

122.54 cm²

34.54 cm²

  • Question 1

What is the area of this shape?

The the answer has been rounded to 2 decimal places (2 d.p)

CORRECT ANSWER
146.14 cm²
EDDIE SAYS
The thing here is to remember tho halve the area of the circle to get the semi circle. This is the bit lots of people forget. The area of the rectangle is 11 x 12 = 121 cm ². The area of the semi circle is Π x 4 x 4 = 50.27 cm² 50.27 cm² ÷ 2 = 25.14 cm² Total area = 121 cm² + 25.14 cm² = 146.14 cm²
  • Question 2

Area of compound shape triangle and semi circle

Calculate the area of this shape.

Round your answer to 2 decimal places.

Write your answer in figures without the units.

CORRECT ANSWER
27.28
EDDIE SAYS
Area of the triangle = 6 x 7 ÷ 2 = 21 cm² Area of the semi circle = Π x 2 x 2 = 12.57 ÷2 = 6.28 cm² Total area = 21 + 6.28 = 27.28 cm² correct to 2 decimal places.
  • Question 3

 

CORRECT ANSWER
 352.47 cm²261.62 cm²129.81 cm²
The area of this shape is
EDDIE SAYS
This was a little sneaky wasn't it. There was no radius given. We could find the diameter of the circle 14 - 5 = 9 cm and then halve it to get the radius of 4.5 cm. Did you spot it? Area of the rectangle = 7 x 14 = 98 cm² Area of the semi circle = Π x 4.5 x 4.5 = 163.62 ÷ 2 = 31.81 cm² Total area = 98 + 31.81 = 129.81 cm² correct to 2 decimal places.
  • Question 4

semi circle and a rectangle

Calculate the area of this shape.

Round your answer to 2 decimal places (2 d.p)

CORRECT ANSWER
EDDIE SAYS
Are you getting used to applying two formulas and adding them up now? Area of the rectangle = 25 x 32 = 800 cm² Area of the semi circle = Π x 12 x 12 = 452.39 ÷ 2 = 226.19 cm² Total area = 800 + 226.19 = 1026.19 cm² correct to 2 decimal places.
  • Question 5

triangle and semi circle

CORRECT ANSWER
 100.45 cm²90 cm²245.96 cm²45 cm²190.48 cm²200.96 cm²100.48 cm²
The area of the triangle is
The area of the semi circle is
Total area is
EDDIE SAYS
Area of the triangle = 10 x 9 ÷ 2 = 45 cm² Area of the semi circle = Π x 8 x 8 = 200.96 ÷ 2 = 100.48 cm² Total area = 45 + 45 + 100.48 = 190.48 cm² correct to 2 decimal places. Did you remember that there were two triangles, but you only had to calculate the area of one. As no other information given on the second triangle we have to assume they are the same size.
  • Question 6

compound area circle and square

Find the area of the shaded green part of the square.

Round your answer to 2 decimal places.

Write your answer in figures without the units.

CORRECT ANSWER
42.06
EDDIE SAYS
Whoa..how do i find the area of those 4 triangle things? Area of the square 14 x 14 = 196 cm² Area of the circle = Π x 7 x 7 = 153.94 cm² Because you only want the area of the green shaded part you subtract the area of the circle from the area of the square. Total area = 196 - 153.94 = 42.06 cm² correct to 2 decimal places.
  • Question 7

CORRECT ANSWER
 58 cm²108.24 cm²66.57 cm²102.65 cm²
The area of this shapes is
EDDIE SAYS
This is straight forward if you know your formulas and spotted that the circle gave you a diameter and not a radius. Area of parallelogram 9 x 6 = 54 cm² Area of circle = π x 2 x 2 = 12.57 cm², Total area = 54 + 12.57 = 66.57 cm²
  • Question 8

Semi circle and triangle

Find the area of this shape.

Round your answer to 2 decimal places.

Write your answer in figures without the units.

CORRECT ANSWER
104.55
EDDIE SAYS
Strange looking shape isn't it. Area of the triangle = 8 x 12 ÷ 2 = 48 cm² Area of the semi circle = Π x 6 x 6 = 113.10 ÷ 2 = 56.55 cm² Total area = 48 + 56.55 = 104.55 cm² correct to 2 decimal places.
  • Question 9

Find the area of the pink shaded triangle.

CORRECT ANSWER
34.54 cm²
EDDIE SAYS
Quite often you will have to subtract when working out areas. Make sure you can spot when. Area of the triangle = 8 x 11 ÷ 2 = 44 cm² Area of the circle = Π x 5 x 5 = 78.54 cm² Total area = 78.54 - 44 = 34.54 cm² correct to 2 decimal places.
  • Question 10

Find the area of the orange shape.

CORRECT ANSWER
EDDIE SAYS
And finally.... Area of rectangle = 10 x 14 = 140 cm² The white part is a semi circle with a radius of 4 cm. Area of the semi circle = Π x 4 x 4 = 50.27 ÷ 2 = 25.14cm² Total area = 140 - 25.14 = 114.86cm² correct to 2 decimal places.
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