Perimeter and area · Usually met around P4
Area of composite shapes
Cut into rectangles, or big rectangle less the gap.
How to do it
Method
Cut into rectangles, or big rectangle less the gap
10 × 7 − 3 × 4 = 70 − 12 = 58
Another way
Cut into two rectangles
10 × 3 + 7 × 4 = 30 + 28 = 58
In full
A rectangle's area = length × width, and a square's = side × side. Backwards, a rectangle's width = area ÷ length, and a square's side is the number that times itself makes the area: 36 cm², 6 × 6 = 36, so the side is 6 cm. A composite shape like an L can be cut into two rectangles, worked out separately and added; or work it out as the big rectangle and take away the missing piece: 10 × 7 − 3 × 4 = 70 − 12 = 58. Both give the same answer, so each checks the other.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A square's area is 4 cm². How long is each side, in cm?
Show the answer and working
Answer: 2 cm
Side × side = 4: 2 × 2 = 4, so the side is 2 cm.
Example 2
A rectangle's area is 56 cm² and its length is 8 cm. How wide is it, in cm?
Show the answer and working
Answer: 7 cm
Length × width = area, so the width is 56 ÷ 8 = 7.
Example 3
Cut the shape into two rectangles to find its area (lengths in cm). Which working is right?
- A. 9 × 11 + 5 × 4
- B. 9 × 11
- C. 9 × 7 + 4 × 4
- D. 9 × 11 − 5 − 4
Choose the right answer
Show the answer and working
Answer: C. 9 × 7 + 4 × 4
The bottom piece is 9 × 7 and the top piece 4 × 4: add them.
Practise it in the game →Perimeter and area · Free to start, unlimited questions, no download