Area and perimeter

A shape is shown on a 1 cm$^2$ grid.

Feb/March 2018

The grid illustration shows a quadrilateral drawn on a $1\text{ cm}^2$ grid.

Feb/March 2019

The diagram presents a composite shape formed by a quarter-circle $OAB$ together with a right-angled triangle $OBC$. The circle has radius $5\,\text{cm}$ and $OC = 6\,\text{cm}$.

Feb/March 2021

On the $1 \text{cm}^2$ grid, sketch one rectangle with perimeter 22 cm and area 24 cm$^2$.

Feb/March 2021

The diagram depicts a smaller circle with radius 7 cm and a larger circle with radius $R$ cm. It is marked NOT TO SCALE. The total area of 16 small circles is equal to the area of one large circle.

Feb/March 2024

The diagram displays trapezium $PQRS$. Its pair of parallel sides are $SR = 5.3$ cm and $PQ = 8.7$ cm. One side that is not parallel is $PS = 4.4$ cm. The indicated height is $3.8$ cm, and a right angle is shown at the base. The figure is labelled NOT TO SCALE.

Feb/March 2024

A shape has been drawn on a grid with 1 $\text{cm}^2$ squares.

Feb/March 2025

A circle with radius 7 cm is compared with a square whose side is x cm. The circle’s circumference has the same length as the square’s perimeter.

Feb/March 2025

A trapezium is drawn, not to scale, and the labels show a left vertical side of 15 cm, an upper sloping side of 10 cm, a right vertical side of 9 cm, and a bottom base of 8 cm. The lower left and lower right corners are right angles.

Feb/March 2025

ABCD forms a square with $AB = (x - 4)$ cm and $BC = 7$ cm. EFG is an isosceles triangle with the equal sides indicated, and each of those equal sides is $(x - 1)$ cm.

May/June 2015

This parallelogram has an area of $51.5\text{ cm}^2$. In the diagram, the base is $x$ cm, the perpendicular height is $5$ cm and the sloping side measures $6$ cm.

May/June 2016

The diagram depicts a trapezium with $AD$ drawn vertically, $AB = 12$ cm, $DC = 8$ cm, $CB = 8$ cm, and a right angle at $A$. The diagram is labelled NOT TO SCALE.

May/June 2016

The diagram depicts a parallelogram. A sloping side is marked 6 cm. The base is marked $x$ cm. Inside the parallelogram, a perpendicular height is marked 5 cm. The diagram is labelled NOT TO SCALE.

May/June 2016

Jared is constructing a house.

May/June 2016

The wildlife park occupies an area of 18 hectares.

May/June 2016

The diagram displays a notice board. NOT TO SCALE. It has the form of a semicircle attached to a square whose side measures 74 cm.

May/June 2017

Work out the area of the shape.

May/June 2018

A triangle is drawn with a base measuring 8.4 cm and a perpendicular height of 3.5 cm. The diagram is not drawn to scale.

May/June 2019

A triangle is drawn and the diagram is NOT TO SCALE. Its base measures $8.4\text{ cm}$, and the perpendicular height is $3.5\text{ cm}$.

May/June 2019

The diagram depicts a trapezium with one line of symmetry. Its top base measures $15.4$ cm, the marked height is $18.2$ cm, and the bottom-left angle is $62^\circ$.

May/June 2021

Calculate the area of this trapezium.

May/June 2022

Calculate the area of a rectangle measuring $9.5\,\text{m}$ in length and $6.8\,\text{m}$ in width.

May/June 2022

Find the area and perimeter for this shape.

May/June 2023

Calculate the area of the shape.

May/June 2023

The diagram represents a figure formed by triangle JKL together with a semicircle whose diameter is JL. JKL is an isosceles right-angled triangle with $JK = JL = 12.8\text{ cm}$. The semicircle has radius $12.8\text{ cm}$. NOT TO SCALE.

May/June 2024

A shape is drawn on a $1\text{ cm}^2$ grid.

May/June 2024

Calculate the area of triangle $ABC$.

May/June 2024

The floor plan of a room in Jo’s house is shown as the shape $ABCDE$. Point $F$ lies within the room.

May/June 2024

Find the area of the trapezium.

May/June 2024

The sketch depicts a trapezium and is NOT TO SCALE. Its area equals $42\text{ cm}^2$. The two parallel sides measure 4 cm and 10 cm, while the perpendicular height is $h$ cm.

May/June 2025

All measurements in this question are given in centimetres. The triangle’s perimeter is equal to the rectangle’s perimeter.

May/June 2025

The diagram represents a figure formed by joining a rectangle and a semicircle. The rectangle measures $16\text{ cm}$ across and $9\text{ cm}$ in height. A semicircle is placed along the top of the rectangle. Its diameter is $10\text{ cm}$. The diagram is labelled NOT TO SCALE.

May/June 2025

ABCD is a trapezium. The diagram indicates DC = 10 cm, AB = 12 cm, and the perpendicular height measures 8 cm (not to scale).

May/June 2025

Leah is laying a gravel path in her garden. The diagram illustrates the path. Its measurements are width $0.8\,\text{m}$, horizontal length $6\,\text{m}$ and vertical length $3\,\text{m}$. One bag of gravel covers an area of $0.5\,\text{m}^2$.

Oct/Nov 2015

The diagram shows a circle whose centre is $O$.

Oct/Nov 2015

The trapezium sketch has parallel sides measuring 13 cm and 16 cm, together with a 4 cm vertical right-hand side and a 5 cm sloping side on the left. It is labelled "NOT TO SCALE".

Oct/Nov 2016

The shaded figure is formed by connecting a square with a rhombus. The square’s side length is 5 cm. The rhombus has a horizontal diagonal measuring 4.5 cm. The diagram is not drawn to scale.

Oct/Nov 2016

The trapezium is drawn with the top edge measuring $13\text{ cm}$, the bottom edge measuring $16\text{ cm}$, the left sloping side measuring $5\text{ cm}$, and the right side being vertical with a length of $4\text{ cm}$. A right angle is indicated at the bottom-right corner. The figure is labelled "NOT TO SCALE".

Oct/Nov 2016

Each of the three shapes has a perimeter of 60 cm. Find $x$ for every part.

Oct/Nov 2016

A triangle has area $528\,\text{cm}^2$, and its base measures $33\,\text{cm}$.

Oct/Nov 2017

A triangle has an area of 528 cm$^2$, and its base measures 33 cm.

Oct/Nov 2017

The diagram depicts the field $ABCD$.

Oct/Nov 2017

The sketch depicts the top view of a table. The shape has right angles marked on it. The upper horizontal side measures $1.2\text{ m}$. The left vertical side drops $0.4\text{ m}$. The right vertical side drops $0.9\text{ m}$. The lower horizontal side measures $0.7\text{ m}$. Diagram not drawn to scale.

Oct/Nov 2018

The diagram depicts a field in the form of a trapezium. AB = 150 m, BC = 90 m and CD = 120 m. Angle ABC = angle BCD = $90^\circ$.

Oct/Nov 2018

Determine the value of $x$.

Oct/Nov 2018

Calculate the area of triangle $PQR$.

Oct/Nov 2018

Determine the perimeter.

Oct/Nov 2019

Triangle $ABC$ is drawn. $AB = 6$ cm. The perpendicular from $C$ to the line through $AB$ is labelled $h$ cm. The diagram is marked NOT TO SCALE. The area of triangle $ABC$ is 27 cm$^2$.

Oct/Nov 2020

The trapezium and the parallelogram have equal areas.

Oct/Nov 2020

Calculate the greatest possible perimeter of the rectangle.

Oct/Nov 2020

A shaded shape is drawn on a grid made up of 1 cm9 squares.

Oct/Nov 2021

A trapezium is drawn. Its upper parallel side measures 7 cm, its height is 12 cm, and its lower parallel side is $y$ cm. Right angles appear at the top right corner and the bottom right corner. The figure is not drawn to scale. This trapezium has an area of 96 $\text{cm}^2$.

Oct/Nov 2021

The diagram depicts a section of land in the form of triangle $ABC$. $AB = 800\,\text{m}$, $AC = 2300\,\text{m}$ and angle $BAC = 30^{\circ}$. The diagram is not drawn to scale. Houses are to be constructed on this land. Each house needs $400\,\text{m}^2$ of land.

Oct/Nov 2021

The diagram represents a trapezium with parallel sides measuring $8.6\text{ cm}$ and $14.2\text{ cm}$, together with a perpendicular height of $7.5\text{ cm}$. NOT TO SCALE.

Oct/Nov 2022

Work out which rectangle has the larger perimeter and how much larger it is.

Oct/Nov 2022

The diagram shows a trapezium with the upper parallel side measuring 8 cm, the lower parallel side measuring 14 cm, and a perpendicular height of 6 cm. It is not drawn to scale.

Oct/Nov 2023

The diagram displays a trapezium whose parallel sides measure 12 cm and $w$ cm. Its height is 8 cm. The area of the trapezium is $78\text{ cm}^2$.

Oct/Nov 2024

The diagram depicts a trapezium. Its lower base measures $6\text{ cm}$. The right-hand vertical side measures $9.5\text{ cm}$. The left-hand vertical side is marked $x\text{ cm}$. Right angles appear at each end of the lower base. NOT TO SCALE. The area of the trapezium is $42\text{ cm}^2$.

Oct/Nov 2024

The diagram depicts a trapezium. It is not drawn to scale. The lower base measures $6\,\text{cm}$. The right vertical side measures $9.5\,\text{cm}$. The left vertical side is marked $x\,\text{cm}$. Right-angle markers are shown at the two bottom corners. The area of the trapezium is $42\,\text{cm}^2$.

Oct/Nov 2024

Find the perimeter of the garden.

Oct/Nov 2024

Calculate the area of triangle ABC.

Oct/Nov 2025

A rectangle has side lengths of 5 cm and 19 cm. Two of these rectangles are placed together to make one shape.

Oct/Nov 2025

A trapezium has parallel sides measuring 6 cm and 14 cm, and the height/left side is 15 cm.

Oct/Nov 2025

The diagram represents a parallelogram. One side measures 6.51 m and a different side measures x m. This parallelogram has the same perimeter as a circle of radius 4 m.

Oct/Nov 2025