Compound shapes and parts of shapes

Determine the total area of the front of his house.

Feb/March 2020

The diagram represents a figure formed by a quarter-circle, OAB, together with a right-angled triangle OBC. The diagram is marked NOT TO SCALE. The circle has radius 5 cm and $OC = 6$ cm.

Feb/March 2021

The diagram depicts a toy. The toy has the form of a cone with radius 4 cm and height 9 cm, placed on a hemisphere with radius 4 cm. Diagram is NOT TO SCALE. Formulae given: The volume, $V$, of a cone with radius $r$ and height $h$ is $V = \frac{1}{3}\pi r^2 h$. The volume, $V$, of a sphere with radius $r$ is $V = \frac{4}{3}\pi r^3$.

May/June 2015

Calculate the area enclosed by triangle $PQR$.

May/June 2023

The figure is built from triangle $JKL$ and a semicircle whose diameter is $JL$. Triangle $JKL$ is an isosceles right-angled triangle with $JK = JL = 12.8$ cm.

May/June 2024

The figure shows a composite shape formed from a square and four congruent isosceles triangles. The square has side length 7.8 cm. The overall height from the top of the upper triangle to the bottom of the lower triangle is 14 cm. The diagram is marked NOT TO SCALE.

May/June 2025

The diagram depicts an equilateral triangle $ABC$ whose three sides each measure $12\text{ cm}$. $ANP$ is a sector of a circle with centre $A$. Point $N$ is on $AC$ so that $AN : NC = 2 : 1$. Point $P$ is on $AB$ so that $AP : PB = 2 : 1$. This diagram is NOT TO SCALE.

May/June 2025

The figure is a pentagon formed by joining two congruent trapeziums. It shows a base of $14\text{ cm}$, a central vertical height of $11.4\text{ cm}$, right angles at the two bottom corners, matching sloping sides indicated by marks, and a left-hand vertical side labelled $x\text{ cm}$. The figure is NOT TO SCALE. Its area is $130.2\text{ cm}^2$.

May/June 2025

The diagram presents the cross section of part of a park bench. It is formed from a rectangle with length $32\text{ cm}$ and width $8\text{ cm}$, together with a curved section. The curved section is formed by two concentric arcs with sector angle $125^{\circ}$. The inner arc has radius $40\text{ cm}$ and the outer arc has radius $48\text{ cm}$. The diagram is labelled "NOT TO SCALE".

Oct/Nov 2016

The shaded figure is formed by joining a square to a rhombus. The square has side length 5 cm, and the rhombus has a diagonal measuring 4.5 cm. The diagram is NOT TO SCALE.

Oct/Nov 2016

The diagram presents a shape assembled from a square and a semi-circle. The square’s bottom edge is labelled 10 cm. The diagram is NOT TO SCALE.

Oct/Nov 2017

A container is constructed from a cylinder and a cone, and each has radius 5 cm. The cylinder has height 12 cm, whereas the cone has height 4.8 cm. The diagram shows the container (NOT TO SCALE). The cylinder is fully filled with water. The container is then inverted, as shown below (NOT TO SCALE). For a cone with radius $r$ and height $h$, the volume $V$ is $V = \frac{1}{3} \pi r^2 h$.

Oct/Nov 2019

A figure is composed of rectangles. Its overall area is $517\text{ m}^2$. The diagram is marked with these lengths: the top is $24\text{ m}$, the right-hand side is $x\text{ m}$, the inner horizontal side is $17\text{ m}$, the inner vertical side is $19\text{ m}$, and the bottom-left side is $7\text{ m}$. NOT TO SCALE.

Oct/Nov 2020

A trapezium whose parallel sides are 8 cm and 14 cm, with a height of 6 cm.

Oct/Nov 2025

The diagram represents a garden. It contains a circular pond, and the shaded region is grass. The grass region’s width matches the pond’s diameter. Width = 10 m, total height = 16 m.

Oct/Nov 2025

An L-shaped figure is drawn, with side lengths of 23 cm, 12 cm, 8 cm, 15 cm, 7 cm and 5 cm.

Oct/Nov 2025