Edexcel IGCSE Math A Higher 4.9 D the Area of Parallelograms and Trapezia Questions

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: 5]

ABCD is a trapezium with one line of symmetry.

Figure for Question Edexcel IGCSE Math A Higher 4.9 D the Area of Parallelograms and Trapezia Questions question 1 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

\text { angle } A D C=60^{\circ} \quad A D=12 \mathrm{~cm} \quad D C=47 \mathrm{~cm}

Work out the area of the trapezium.
Give your answer correct to 3 significant figures.
Show your working clearly.
$\mathrm{cm}^{2}$

Figure for Answer to Question Edexcel IGCSE Math A Higher 4.9 D the Area of Parallelograms and Trapezia Questions question 1 — Edexcel IGCSE Math A Higher

Height of the trapezium:
$12\sin60^\circ=6\sqrt3=10.392\ldots$

Horizontal base of each end triangle:
$12\cos60^\circ=6$

AB=47-6-6=35

Area of the trapezium:
$\frac12(47+35)(6\sqrt3)=426.084\ldots$

Final answer:
$426\text{ cm}^2$

M1 for a method to find the height of the trapezium or the area of triangle ADC. M1 independently for a method to find the base of the triangle. M1 dependent on the previous method mark for finding AB. M1 for a complete method. A1 dependent on M1; allow 420 to 427 from correct working. Working required.

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Edexcel IGCSE Math A Higher 4.9 D the Area of Parallelograms and Trapezia Questions question 1