CAIE IGCSE Mathematics Extended Compound Area and Perimeter

Practise finding areas and perimeters of compound figures by combining straight-sided regions with arcs, sectors and circular parts.

Exam points

decompose the figure into squares, triangles or sectors and calculate each required area
add straight exterior edges and the correct fraction of each circumference for perimeter

[Maximum number: 4]

Figure for Question E5.5.1 Carry out calculations and solve problems involving perimeters and question 1 — CAIE IGCSE Mathematics Extended

NOT TO SCALE

The diagram shows a shape ABQP made from three straight lines and an arc of a sector of a circle. The sector has centre O and angle $90^{\circ}$ .
POQ is a straight line and $A P=P O=O Q=Q B=5 \mathrm{~cm}$ .
Find the area of ABQP.
Give your answer in the form $a+k \pi$ .
$\mathrm{cm}^{2}$

$25+\frac{25\pi}{2}$
M2 for $\frac{90}{360}\times\pi\times(\sqrt{5^2+5^2})^2$
or M1 for $\text{radius}^2=5^2+5^2$
M1 for triangle area $[2\times]\frac{1}{2}\times5\times5$ oe

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E5.5.1 Carry out calculations and solve problems involving perimeters and question 1