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Finding the Area of compound shapes (all 2D shapes)

In this worksheet, students will use the areas of Rectangles, Triangles, Parallelograms and Trapeziums to find the Area of compound shapes.

'Finding the Area of compound shapes (all 2D shapes)' worksheet

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Solve Problems Involving Perimeters and Areas of 2D Shapes

Difficulty level:  

Worksheet Overview

There are five shapes (Rectangles, Triangles, Parallelograms, Trapeziums and Circles) which you will need to be able to find the Area of. 

We will not be using circles today so let's quickly remind ourselves of the formulae for the other four shapes we will be using.

 

REVIEW

  • Rectangles: The area of a Rectangle is given by Area = Base x Height (A=bh).                      

 

  • Triangles: The Area of a Triangle is given by Area = 1/2 x Base x Perpendicular Height (A = bh/2).
    • Be careful of two things here:
      • You MUST use the perpendicular height (The one at 90o to the base).
      • You MUST divide by 2.

  • Parallelograms: The Area of a Parallelogram is given by Area = Base x Perpendicular Height (A=bh).

  • Trapeziums. The area of a Trapezium is given by Area = 1/2 x Sum of the Parallel Sides x Perpendicular Height (1/2 x (a + b) x h).
    • Be careful of two things here:
      • You must divide by 2.
      • a and b are the parallel sides, remember that they could be the sides instead of the top and bottom.

 

EXAMPLE: Find the Area of this compound shape.

 

  • Split the shape into two or more shapes that we can deal with. In this case, it splits nicely into two rectangles.
  • Work out the lengths we are not given. We may not need them, but it's useful to have them in case we do.
  • Label the shapes separately so you know which one you are talking about in your working.

  • The base of A is 5cm and the height of A is 15cm. The Area of A is 75cm2.
  • The base of B is 3cm and the height of B is 4cm. The Area of B is 12cm2.
  • The total Area of the shape is 75cm2 + 12cm2 = 87cm2.

In this worksheet, use your knowledge to calculate the Area of each shape. 

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