Area and perimeter

A rectangle and a triangle are drawn on a square grid.

Work out the ratio area of rectangle: area of triangle

Five identical spheres just fit inside a cylinder. Each sphere has radius r.

What fraction of the space inside the cylinder is filled by the spheres? You must show your working.

Here is a solid prism.

How many faces does the prism have?

The prism has volume = 3500cm³ and length = 20 cm

Work out the area of the cross-section of the prism.

Here is a solid prism.

How many faces does the prism have?

The prism has volume = 3500cm³ and length = 20 cm

Work out the area of the cross-section of the prism.

Work out the area of this triangle.

ABCDE is a pentagon with AB = 7 cm

AB and BC are perpendicular.

AB and DC are equal and parallel.

Area of the pentagon = 54 cm²

The pentagon has exactly one line of symmetry.

Complete a labelled drawing of the pentagon.

Here is a right-angled triangular prism.

The ratio of the edges is a: b: c: d = 3: 4: 5: 12

Work out the total length of all of the edges of the prism.

The front elevation of a cuboid is shown on this centimetre grid.

Draw the side elevation on this centimetre grid.

The front elevation of a cuboid is shown on this centimetre grid.

Draw the side elevation on this centimetre grid.

A cylinder, C, and a sphere, S, each have radius r C has height h

volume of C = volume of S

Work out the ratio r: h You must show your working.

A different cylinder has radius 3 r and height 2 h.

How many times bigger is the volume of this cylinder than the volume of C?

In the diagrams, all lengths are in centimetres.

The two shapes have equal areas.

Work out k: m

The boundaries of a city form a trapezium.

The population density of the city is 9450 people per square kilometre.

Work out the number of people who live in the city.

Here is a prism drawn on an isometric grid.

Work out the volume of the prism.

Here is a prism drawn on an isometric grid.

Work out the volume of the prism.

Here is a right-angled triangle on a centimetre grid.

Write down the coordinates of the midpoint of the longest side.

Work out the area of the triangle.

Here is a cuboid.

Work out the volume of the cuboid. Give your answer to 1 decimal place.

An open cardboard cylinder has radius 1.9 cm and height 10.2 cm

Harry assumes that the net of the cylinder is a rectangle with length l cm

Work out the area of this rectangle.

In fact, the net is a parallelogram, not a rectangle. Not drawn

What does this mean about the area of the net? Tick one box.

What does this mean about the perimeter of the net? Tick one box.

Here is a square.

Use a ruler to measure a side length of the square. Give your answer in millimetres.

Here is a quadrilateral.

Use a protractor to measure the size of the smallest angle.

A different quadrilateral is drawn on a centimetre grid.

By counting squares, work out the area of the quadrilateral.

One side of a rectangle is drawn on this centimetre grid.

Complete the rectangle so that it has a perimeter of 20 cm

ABCD is a trapezium. All four sides are different lengths. AB is parallel to CD. The diagonals intersect at X.

For each statement, tick the correct box.

Work out the length of the rectangle.

In this right-angled triangle, a = 16 cm a: c = 4: 5 Work out the area of the triangle.

A solid shape is made from centimetre cubes. The front elevation and side elevation of the shape are shown.

the maximum possible number of cubes in the shape and the minimum possible number of cubes in the shape.

A diagonal of a rectangle is drawn on a centimetre grid. The sides of the rectangle are on the grid lines.

Work out the area of the rectangle.

One side of a parallelogram is drawn on this centimetre grid. The parallelogram does not have any right angles. Complete the parallelogram so that it has area 24 cm²

Two sides of a rhombus are drawn on this grid. Complete the rhombus.

Here is a cuboid. w, x and y are different whole numbers.

The total length of all the edges of the cuboid is 80 cm The volume is greater than 200 cm³ Work out one possible set of values for w, x and y.

Here is a solid cube.

Circle the expression for the total surface area in cm²

Here is a cuboid. w, x and y are different whole numbers.

The total length of all the edges of the cuboid is 80 cm The volume is greater than 200 cm³ Work out one possible set of values for w, x and y.

Here is a solid cube.

Circle the expression for the total surface area in cm²

Trapezium DEFG is formed by joining triangle DEH

ABC is similar to DEH. Work out the area of DEFG.

ABCDE is a pentagon.

Work out the area of the pentagon.

ABCDE is a pentagon.

Work out the area of the pentagon.

Here are two solid cubes, X and Y. The mass of X is 10.976 kg The area of each face of X is 784 cm²

Zayan wants to know the density of Y. He assumes that Y is identical to X.

What density should he get for Y? Give your answer in grams per cubic centimetre.

In fact, the mass of Y is less than the mass of X the area of each face of Y is greater than the area of each face of X.

What does this mean about the actual density of Y? Tick one box.

A shape is made by joining a right-angled triangle to a rectangle.

Work out the area of the shape.

A shape is made by joining a right-angled triangle to a rectangle.

Work out the area of the shape.

An empty container is a cylinder of radius 3.5 cm and height 40 cm A tennis ball is a sphere of radius 3.5 cm Will six of the tennis balls fit in the container? Tick a box.

Show working to support your answer.

Information about two fridge-freezers, A and B, is shown.

Grace buys one of these fridge-freezers. She buys the one with the greater freezer capacity. Which one does she buy? You must show your working.

Information about two fridge-freezers, A and B, is shown.

Grace buys one of these fridge-freezers. She buys the one with the greater freezer capacity. Which one does she buy? You must show your working.

Here is a scale drawing of a reservoir. Scale: 1 cm represents 500 m

Virat wants to estimate the volume of water in the reservoir. He draws on the scale drawing a circle with radius 3 cm

Virat estimates the volume of the reservoir by assuming that

• the reservoir is a cylinder whose cross section is the circle

• the depth of the reservoir is 17 metres.

Work out Virat’s estimate in cubic metres.

In fact,

• the depth of the reservoir is 13.8 metres

• the reservoir is not a cylinder (see diagram).

Which statement about the actual volume of the reservoir is correct? Tick one box.

Give a reason for your answer.

The vertices of a regular hexagon lie on a circle with centre O and radius 5 cm

Work out the shaded area.

Here is a cuboid.

Work out the volume.

Work out the area of this triangle.

A circle has a radius of 11.5 cm

Work out the area of the circle.

A box is the shape of half a cylinder on top of a cuboid.

Work out the volume of the box.

Here is a shape made from rectangles.

Work out the area.

Zak wants to work out the area of this triangle.

Here is his working.

What is wrong with his method?

Here is a cuboid.

Assume that the total surface area of the cuboid is 200 cm 2 Work out the volume of the cuboid.

In fact, the total surface area of the cuboid is smaller than 200 cm² What does this mean about the volume of the cuboid? Tick one box.

Here is a cuboid.

Assume that the total surface area of the cuboid is 200 cm 2 Work out the volume of the cuboid.

cm 3

In fact, the total surface area of the cuboid is smaller than 200 cm² What does this mean about the volume of the cuboid? Tick one box.

The diagram shows a wall.

The area of the wall is 39.2 m 2 Work out the length of the wall.

Right-angled triangle ABC is the cross section of a prism. AB = 5 cm BC = 12 cm M is the midpoint of CF. AM = 16 cm

Work out the volume of the prism.

Here is a cuboid.

The two largest faces are blue. The other four faces are green. Is the total blue area greater than the total green area? You must show your working.

Here is a small cuboid and a cube.

Small cuboids and cubes are stacked in layers to make larger cuboids. Here is a cuboid made with four layers.

The pattern is continued to make a cuboid with volume 336 cm³ How many cubes are used?

Tom is tiling a wall. He needs to buy at least 100 tiles. The tiles are sold in large packs and small packs.

Large pack 40 tiles £18 Small pack 28 tiles £14 Special offer 25% reduction when you buy 3 or more large packs

Work out the cheapest cost for Tom to buy the packs of tiles he needs.

Tom is also tiling a floor. The floor is a rectangle with length 600 cm and width 240 cm Each tile is a square with side 40 cm Tom uses this method to work out the number of tiles he needs.

Number of tiles that will fit along the width = 240 ÷ 40 = 6 Total number of tiles needed = 15 + 6

Give a reason why Tom’s method is wrong.

Here is a triangular sail.

Vicky needs to buy waterproofing liquid for the sail. She will put 3 coats of liquid on each side of the sail. A litre of liquid covers 8.5 square metres of sail. How many 1-litre bottles of liquid does Vicky need?

Another sail is joined to the first sail as shown.

x is an acute angle. Work out the size of angle x.

Here is a cuboid.

Work out the volume.

Work out the area of the trapezium.

Circle the volume, in cm³, of a cylinder with radius 5 cm and height 8 cm 40 π 80 π 200 π 1600 π

Ashraf is going to put boxes into a crate. The crate is a cuboid measuring 2.5 m by 2 m by 1.2 m Each box is a cube of length 50 cm He does these calculations.

He claims, ‘‘I can put 48 boxes in the crate.’’ Evaluate Ashraf’s method and claim.

A large rectangle is made by joining three identical small rectangles as shown.

The perimeter of one small rectangle is 15 cm Work out the perimeter of the large rectangle.

Some concrete has volume 3.8 m³

The density of the concrete is 2400 kg/m³ Work out the mass of the concrete.

The 3.8 m³ of concrete is made into the shape of a cylinder. The base has radius 0.5 metres.

Work out the height of the cylinder.

Work out the area of the triangle.

Three identical isosceles triangles are joined to make this trapezium. Each triangle has base b cm and perpendicular height h cm

Work out an expression, in terms of b and h, for the area of the trapezium. Give your answer in its simplest form.

This diagram shows the same trapezium.

b: s = 2: 3 Work out an expression, in terms of b, for the perimeter of the trapezium.

Three identical isosceles triangles are joined to make this trapezium. Each triangle has base b cm and perpendicular height h cm

Work out an expression, in terms of b and h, for the area of the trapezium. Give your answer in its simplest form.

This diagram shows the same trapezium.

b: s = 2: 3 Work out an expression, in terms of b, for the perimeter of the trapezium.

A, B and C are points on the axes as shown.

The area of triangle ABC is 28 square units. Work out possible coordinates for A, B a nd C.

The graph shows information about prisms with the same volume.

Give one example to show the volume is 24 cm³

The diagram shows a prism with volume 24 cm³ The height of the triangular cross section is h.

Work out the height, h.

The graph shows information about prisms with the same volume.

Give one example to show the volume is 24 cm³

The diagram shows a prism with volume 24 cm³ The height of the triangular cross section is h.

Work out the height, h.

Work out the area of the parallelogram.

ABC is a right-angled triangle. A is the point (–3, –2) B is the point (1, –2) C is a point on the line y = 4

Draw triangle ABC on the centimetre grid below.

Work out the area of triangle ABC.

Eva thinks she can save water by having a shower instead of a bath. Eva’s shower uses 10.8 litres per minute lasts for 8 minutes. Eva assumes that the water in her bath is in the shape of this cuboid.

Using Eva’s assumption, work out how many litres of water she saves by having a shower instead of a bath.

A shows the water level before Eva gets into the bath. B shows the cuboid in the empty bath.

What does this tell you about the amount of water saved?

Circle the area that is equal to 36 mm²

Each shape below has an area of 24 cm² Complete the missing lengths.