GCSE Maths revision · Geometry and measures

Area of 2D shapes

Foundation and Higher

The idea

Area of a rectangle $= lw$ , triangle $= \tfrac{1}{2}bh$ , parallelogram $= bh$ and trapezium $= \tfrac{1}{2}(a + b)h$ . The height is always perpendicular to the base.

Split a compound shape into rectangles and triangles.
Find each area using its perpendicular height.
Add (or subtract for a hole) and give square units.

Watch out Use the perpendicular height, never a sloping side.

See it worked

Worked exampleNon-calculator2 marks

A triangle has base 14 cm and perpendicular height 9 cm. Work out its area.

$14\times 9/2$
The area of a triangle is half $\times$ base $\times$ perpendicular height.
Area = $\frac{1}{2}$ $\times$ 14 $\times$ 9 = 63 cm².

Answer $63\,\mathrm{cm^{2}}$

Your turn

Question 1Non-calculator4 marks

A garden is in the shape of a trapezium. Its parallel sides are 9 m and 15 m long, and they are 8 m apart. Turf costs £4.50 per square metre.

Work out the cost of turf to cover the whole garden.

Question 2Non-calculator4 marks

A 9 m by 7 m rectangle has a 3 m by 3 m rectangular corner removed.

(a) Find the remaining area.

(b) Find the perimeter of the remaining L-shape.

Question 3Non-calculator4 marks

A square has sides of length $2x$ cm. A right-angled triangle with shorter sides $x$ cm and $x$ cm is cut from one corner. The area of the shape that is left is $56\text{ cm}^2$ .

(a) Find the value of $x$ .

(b) Work out the area of the triangle that was cut off.

In past papers

220 official questions in 157 papers since 2017. The latest:

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