Edexcel IGCSE Math A 4.9.D Areas of Parallelograms & Trapezia

Practise calculating or reversing parallelogram and trapezium area formulae in direct and composite-shape diagrams.

Exam points

use perpendicular height rather than a sloping side in each area formula
derive a shared height from a parallelogram before calculating an adjacent trapezium
rearrange the trapezium formula to find a missing parallel side or height

[Maximum number: 2]

The area of land on a farm is 120 hectares.
The farmer grows crops on $\frac{7}{8}$ of the land.
On $\frac{2}{3}$ of the land used to grow crops, the farmer grows wheat.

Here is a diagram of one field on the farm.

Figure for Question 4.9.D The area of parallelograms and trapezia question 1 — Edexcel IGCSE Math A Foundation

Diagram NOT accurately drawn

The field is in the shape of a trapezium.
The lengths of the parallel sides are 80 m and 120 m.
The distance between the parallel sides is 110 m.

Work out the area of this field.
Give your answer in $\mathrm{m}^{2}$ .

\frac{1}{2}\times(120+80)\times110=11000

80\times110+2\times\frac{1}{2}\times\frac{1}{2}\times(120-80)\times110=11000

Final answer:

11000\text{ m}^2

M1 for a complete method involving a rectangle and two triangles.
A1.

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4.9.D The area of parallelograms and trapezia question 1