Edexcel IGCSE Math A 4.9 mensuration of 2D shapes

Use this mensuration page to calculate perimeters, areas, circle circumferences and sectors, including shapes built from rectangles, triangles and circles.

Exam points

Calculate perimeters of rectangles, compound shapes and shapes drawn on grids.
Find areas of triangles, rectangles, trapezia and compound shapes from diagrams.
Use circle formulae for circumference, area, sectors or shaded regions.

Covered syllabus points

4.9.A Measurements within the metric system 4.9.B Perimeters of triangles and rectangles 4.9.C Areas of triangles and rectangles 4.9.D The area of parallelograms and trapezia 4.9.E Circumferences and areas of circles using relevant 4.9.HA Perimeters and areas of sectors of circles Radian

[Maximum number: 4]

The diagram shows rectangle ABCD

Figure for Question 4.9 Mensuration of 2D shapes question 1 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

Work out the perimeter of the rectangle.
Show your working clearly.
cm

5x-1=3x+7.4x=4.2

Perimeter:
$2\times24+2(5\times4.2-1)=88$

Final answer:
88

[Maximum number: 6]

The diagram shows a quadrilateral ABCD

Figure for Question 4.9 Mensuration of 2D shapes question 2 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

In the diagram, ABC and DAC are right-angled triangles.

B C=6 \mathrm{~cm} \quad A C=7.5 \mathrm{~cm}

The area of quadrilateral ABCD is $31.5 \mathrm{~cm}^{2}$
Work out the length of AD
cm

$AB=\sqrt{7.5^{2}-6^{2}}=4.5$ $\text{Area }ABC=\frac12\times6\times4.5=13.5$ $\text{Area }DAC=31.5-13.5=18$ $AD=\frac{18}{7.5}\div0.5=4.8$

Final answer:
4.8

Accept 4.78 to 4.81.

ABCD is a trapezium with one line of symmetry.

\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.
$\mathrm{cm}^{2}$

All question bank results loaded

Covered syllabus points

4.9 Mensuration of 2D shapes question 1

4.9 Mensuration of 2D shapes question 2

4.9 Mensuration of 2D shapes question 3