Area and perimeter

Here is a plan of part of Macsen’s garden. There is a circle inside a triangle. The circle has a diameter of 7 m.

Macsen will cover the shaded area with gravel. Gravel is sold in bags. Each bag of gravel covers an area of 12.5 m²

Work out the number of bags of gravel Macsen will need.

Macsen finds that each bag of gravel only covers an area of 11 m²

How does this affect your answer to part (a)?

Here is a plan of part of Macsen’s garden. There is a circle inside a triangle. The circle has a diameter of 7 m.

Macsen will cover the shaded area with gravel. Gravel is sold in bags. Each bag of gravel covers an area of 12.5 m²

Work out the number of bags of gravel Macsen will need.

Macsen finds that each bag of gravel only covers an area of 11 m²

How does this affect your answer to part (a)?

The diagram shows trapezium ABCD.

AB = 12 cm AD = 8 cm The trapezium has an area of 112 cm² Work out the perimeter of the trapezium. Give your answer correct to 3 significant figures.

The diagram shows trapezium ABCD.

AB = 12 cm AD = 8 cm The trapezium has an area of 112 cm² Work out the perimeter of the trapezium. Give your answer correct to 3 significant figures.

The diagram shows triangle ABC.

In the diagram, all measurements are in centimetres. AC = BC The perimeter of the triangle is 72 cm. Work out the area of the triangle.

The diagram shows triangle ABC.

In the diagram, all measurements are in centimetres. AC = BC The perimeter of the triangle is 72 cm. Work out the area of the triangle.

ABC and AED are straight lines. BE and CD are parallel.

BE = 4.2 cm CD = 6.3 cm AC = 10.8 cm Work out the area of trapezium BCDE.

A playground is in the shape of a right-angled triangle.

Dan makes a scale drawing of the playground. He uses a scale of 1 cm represents 5 m The area of the playground on the scale drawing is 28 cm² The real length of QR is 40 m Work out the real length of PQ.

Milo is trying to find the area of this rectangle.

He writes, “The area is 400 cm² because 5 × 4 × 5 × 4 = 400”

Explain what is wrong with Milo’s method.

Anya works out the area of a shape. Her answer is 86 cm.

Explain why her answer cannot be fully correct.

Here is a shape made from a rectangle and a triangle.

The shape has exactly one line of symmetry. The area of the rectangle is 3.5 times the area of the triangle. The width of the rectangle is w cm. Work out the value of w. You must show all your working.

The diagram shows a solid cylinder on a horizontal floor.

The cylinder has a volume of 1200 cm³ height of 40 cm. The cylinder exerts a force of 90 newtons on the floor. Work out the pressure on the floor due to the cylinder.

Here is a triangle and a rectangle.

All measurements are in centimetres. The area of the triangle is 10 cm² greater than the area of the rectangle. Work out the value of x.

Here is a triangle and a rectangle.

All measurements are in centimetres. The area of the triangle is 10 cm² greater than the area of the rectangle. Work out the value of x.

The diagram shows a plan of Jason’s garden. ABCO and DEFO are rectangles. CDO is a right-angled triangle. AFO is a sector of a circle with centre O and angle AOF = 90°

Jason is going to cover his garden with grass seed. Each bag of grass seed covers 14 m² of garden. Each bag of grass seed costs £10.95 Work out how much it will cost Jason to buy all the bags of grass seed he needs.

The diagram shows a plan of Jason’s garden. ABCO and DEFO are rectangles. CDO is a right-angled triangle. AFO is a sector of a circle with centre O and angle AOF = 90°

Jason is going to cover his garden with grass seed. Each bag of grass seed covers 14 m² of garden. Each bag of grass seed costs £10.95 Work out how much it will cost Jason to buy all the bags of grass seed he needs.

The diagram shows two similar solid triangular prisms, A and B.

The volume of prism A is 58.806 cm³ The volume of prism B is 1587.762 cm³ The cross section of each prism is a right-angled triangle. For prism B the length of the base of the triangle is 8.1 cm the area of the triangle is 43.74 cm² The height of the triangle for prism A is hcm. Work out the value of h.

16On the centimetre grid, draw an isosceles triangle with an area of 12 cm²

The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm.

The area of trapezium QUVR is Acm² Show that A = 2x² + 20x

The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm.

The area of trapezium QUVR is Acm² Show that A = 2x² + 20x

The diagram shows a prism.

The cross section of the prism is a right‑angled triangle. The base of the triangle has length 5 cm The prism has length 25 cm The prism has volume 750 cm³ Work out the height of the prism.

The diagram shows a prism.

The cross section of the prism is a right‑angled triangle. The base of the triangle has length 5 cm The prism has length 25 cm The prism has volume 750 cm³ Work out the height of the prism.

Here is trapezium ABCD.

The area of the trapezium is 66 cm² the length of AB: the length of CD = 2: 3 Find the length of AB.

This diagram shows two squares.

Work out the area of the square shown shaded in the diagram.

The diagram shows a sector OPQR of a circle, centre O and radius 8 cm.

OPR is a triangle. Work out the area of the shaded segment PQR. Give your answer correct to 3 significant figures.

The diagram shows a sector OPQR of a circle, centre O and radius 8 cm.

OPR is a triangle. Work out the area of the shaded segment PQR. Give your answer correct to 3 significant figures.

29The diagram shows a solid triangular prism.

The prism is made from wood with a density of 0.8 g/cm³ Work out the mass of this prism.

The diagram shows a prism.

The cross section of the prism has exactly one line of symmetry. Work out the volume of the prism. Give your answer correct to 3 significant figures.

The diagram shows a parallelogram.

The area of the parallelogram is greater than 15 cm²

Find the range of possible values of x.

Here are two squares, A and B.

The length of the side of square A is 50% of the length of the side of square B. Express the area of the shaded region of square A as a percentage of the area of square B.

A square has an area of 81 cm²

Find the perimeter of the square.

The diagram shows a right-angled triangle and a parallelogram.

The area of the parallelogram is 5 times the area of the triangle. The perpendicular height of the parallelogram is h cm.

Find the value of h.

The diagram shows a floor in the shape of a trapezium.

John is going to paint the floor.

Each 5 litre tin of paint costs £16.99 1 litre of paint covers an area of 2 m²

John has £160 to spend on paint.

Has John got enough money to buy all the paint he needs? You must show how you get your answer.

The diagram shows a floor in the shape of a trapezium.

John is going to paint the floor.

Each 5 litre tin of paint costs £16.99 1 litre of paint covers an area of 2 m²

John has £160 to spend on paint.

Has John got enough money to buy all the paint he needs? You must show how you get your answer.

The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3: 4: 5

Work out the area of the triangle.

Here is a triangular prism.

Work out the volume of the prism. Give your answer correct to 3 significant figures.

ABC is an isosceles right-angled triangle.

The area of the triangle is 162 cm²

Work out the value of x.

The length of a rectangle is twice as long as the width of the rectangle. The area of the rectangle is 32 cm².

Draw the rectangle on the centimetre grid.

The diagram shows two shapes drawn on a centimetre grid.

Find the area of shape P.

Write down the mathematical name of quadrilateral Q.