Area and perimeter

The diagram depicts a trapezium with side lengths measured in centimetres. Its area is $120\text{ cm}^2$.

May/June 2015

In trapezium $ABCD$, $AB$ runs parallel to $DC$. $DB$ and $AC$ are straight lines.

May/June 2015

Every angle is a right angle. Every length is given in centimetres.

May/June 2017

$ABCDE$ represents the building’s cross-section. Every length is measured in metres.

May/June 2017

The diagram represents trapezium $ABCD$. The lengths $AB = 7\text{ cm}$ and $DC = 10\text{ cm}$ are given. The area of $ABCD$ is $85\text{ cm}^2$. The perpendicular height of the trapezium is $h\text{ cm}$.

May/June 2021

For this question, every dimension is measured in centimetres.

May/June 2024

The diagram depicts a trapezium, and the lengths are given in centimetres.

May/June 2025

ABCD is a quadrilateral in which BC is parallel to AD. CD is perpendicular to BC. BC = 5 cm and AD = 12 cm. The area of triangle BCD is 20 cm$^2$.

Oct/Nov 2015

ABCD is a trapezium with $AB$ parallel to $DC$. $DC = 15\text{ cm}$ and $AB = x\text{ cm}$. The perpendicular distance between $AB$ and $DC$ is $3\text{ cm}$ shorter than the length of $AB$. The area of $ABCD$ is $75\text{ cm}^2$.

Oct/Nov 2015

The diagram depicts a square card with a triangle and two small squares cut away. Every length on the diagram is measured in centimetres.

Oct/Nov 2016

$ABCD$ forms a rectangle with $AB = 10$ cm and $AD = 12$ cm. $PQ$ runs parallel to $AB$ and $RS$ runs parallel to $AD$. The intersection of $PQ$ and $RS$ is $Y$. $BR = DP = x$ cm. A smaller rectangle and a square are shaded.

Oct/Nov 2019

A regular hexagon has the same perimeter as a regular octagon. Each side of the octagon measures $9\text{ cm}$. Determine the length of one side of the hexagon.

Oct/Nov 2022