Area & perimeter

The diagram shows a plan of a garden made from three identical rectangles.

The length of each rectangle is 6 metres. The width of each rectangle is 3.5 metres.

Jeremy puts a fence around the perimeter of the garden. He charges 7.60 euros for each 1 metre of fence.

Work out how much Jeremy charges in total for the fence.

The diagram shows the plan of a stage.

The stage is made up of a rectangle and an isosceles triangle.

Yuko is going to cover the stage with varnish. She needs to buy enough tins of varnish to cover the stage with one coat of varnish.

Each tin of varnish covers an area of 4 m²

Work out the smallest number of tins of varnish that Yuko needs to buy. Show your working clearly.

ABCD is a trapezium with one line of symmetry.

angle ADC = 60° AD = 12 cm DC = 47 cm

Work out the area of the trapezium. Give your answer correct to 3 significant figures. Show your working clearly.

ABCD is a trapezium with one line of symmetry.

angle ADC = 60° AD = 12 cm DC = 47 cm

Work out the area of the trapezium. Give your answer correct to 3 significant figures. Show your working clearly.

The diagram shows a quadrilateral ACDF

ABEF is a trapezium.

BCDE is a parallelogram.

FE = 26 cm AB = 18 cm BC = 12 cm

The area of the parallelogram BCDE is 96 cm²

Work out the area of the trapezium ABEF

The diagram shows two triangles, ADE and CDB

ABD is a straight line.

AE = 28 cm ED = 45 cm AB = 21 cm CD = 35 cm

angle AED = angle CBD = 90°

Work out the area of triangle CDB Give your answer correct to 3 significant figures.

The diagram shows a shape ABCDE made from a right-angled triangle ABE and a

ABC is a straight line.

AB = 15 cm AE = 17 cm

The perimeter of triangle ABE is 40 cm

Work out the area of the shape ABCDE

The diagram shows a trapezium, ABCD

DAB and ADC are right angles.

AD = 15 cm DC = 14 cm

The area of the trapezium is 360 cm²

Work out the perimeter of the trapezium.

The diagram shows a trapezium, ABCD

DAB and ADC are right angles.

AD = 15 cm DC = 14 cm

The area of the trapezium is 360 cm²

Work out the perimeter of the trapezium.

The diagram shows a hexagon ABCDEF

Angle BCF = 30° AB, FC and ED are parallel.

Calculate the area of ABCDEF Show your working clearly.

Here is a centimetre grid.

On the grid, draw a right-angled triangle.

Here is a centimetre grid.

On the grid, draw a rectangle with an area of 20 cm²

The diagram shows a hexagon ABCDEF

AB = 25 cm BC = (x + 2) cm CD = 8 cm EF = 7 cm AF = (x + 6) cm

The area of hexagon ABCDEF is 258 cm²

Work out the value of x

The diagram shows a rectangle measuring 10 cm by 3 cm.

A shape is made by placing 3 of these rectangles together as shown in the diagram.

Work out the perimeter of the shape.

13The diagram shows the plan of a garden.

Martyn covers the garden with square tiles of side length 50 cm. There are no gaps between the tiles.

It takes 4 minutes to lay each tile.

Work out how long it takes Martyn to cover the whole garden with tiles. Give your answer in hours and minutes.

The diagram shows a rectangle and an isosceles triangle.

The perimeter of the rectangle is equal to the perimeter of the triangle.

Find the area of the rectangle.

The diagram shows a cuboid.

The volume of the cuboid is 231 cm³

Calculate the value of w

The diagram shows a shaded shape AEBCD made by removing triangle AEB from

AE = 7.2 cm BE = 5.4 cm BC = 6 cm angle AEB = 90°

Work out the perimeter of the shaded shape.

Here is a floor plan of a stage. The plan is formed from a triangle and a rectangle.

The stage manager is going to paint the floor.

One tin of paint covers an area of 1.8 m² One tin of paint costs $16.40

Paint can only be bought in full tins.

The stage manager has $190 to spend.

Does the stage manager have enough money to buy enough tins to paint all of the floor? Show your working clearly.

The diagram shows a solid triangular prism.

Work out the total surface area of the triangular prism. Give your answer correct to 3 significant figures.

The diagram shows an isosceles triangle ABC

AB = 7 cm AC = BC = ycm

The area of the triangle is 42 cm²

Work out the value of y

The diagram shows the plan of a floor.

Indira is going to paint the floor. She needs to buy enough tins of paint to cover the floor with one coat of paint.

Each tin of paint covers an area of 7 m² Each tin of paint costs £23.90

Indira buys the least possible number of tins of paint.

Work out the total cost of the tins of paint that Indira buys. Show your working clearly.

The diagram shows rectangle ABCD

Work out the perimeter of the rectangle. Show your working clearly.

The diagram shows an isosceles triangle, with base length 24 cm.

The perimeter of the triangle is 54 cm.

Work out the area of the triangle.

The diagram shows an isosceles triangle, with base length 24 cm.

The perimeter of the triangle is 54 cm.

Work out the area of the triangle.

The diagram shows a shape ABCDEFG made from a square ABDF and three identical isosceles triangles BCD, DEF and FGA.

The perimeter of the square ABDF is 48 cm. The perimeter of each isosceles triangle is 30 cm.

Work out the perimeter of the shape ABCDEFG.

The diagram shows a quadrilateral ABCD

In the diagram, ABC and DAC are right‑angled triangles.

BC = 6 cm AC = 7.5 cm

The area of quadrilateral ABCD is 31.5 cm²

Work out the length of AD

The diagram shows a trapezium.

Work out the area of the trapezium.

The diagram shows a classroom wall in the shape of a trapezium.

Dion wants to paint the classroom wall completely twice. He knows that each tin of paint will cover 12 m²

He is going to have to buy all the paint he needs.

Work out the least number of tins of paint that Dion will need to buy. Show your working clearly.

The diagram shows isosceles triangle ABC

AB = AC = 17.5 cm
BC = 28 cm

Calculate the area of triangle ABC

The diagram shows isosceles triangle ABC

AB = AC = 17.5 cm
BC = 28 cm

Calculate the area of triangle ABC

Here is a square.

The perimeter of the square is 24 cm.

The shaded rectangle below is made from 4 of these squares.

Work out the perimeter of the shaded rectangle.

Here is a rectangle.

(2 x + 3) cm
Diagram NOT

Given that the area of the rectangle is less than 75 cm²

find the range of possible values of x

The diagram shows two congruent triangles, ABC and DEF, drawn on a centimetre grid.

Find the area of the region R, shown shaded in the diagram.

The diagram shows the front of a wooden door with a semicircular glass window.

Julie wants to apply 2 coats of wood varnish to the front of the door, shown shaded in the diagram.

250 millilitres of wood varnish covers 4 m² of the wood.

Work out how many millilitres of wood varnish Julie will need. Give your answer correct to the nearest millilitre.

ABCDEF and GHIJKL are regular hexagons each with centre O.

GHIJKL is an enlargement of ABCDEF, with centre O and scale factor 2 OA = a OB = b

Write the following vectors, in terms of a and b. Simplify your answers.

AB

KI

LD

The triangle OAB has an area of 5 cm²

Calculate the area of the shaded region.

ABCED is a five-sided shape.

ABCD is a rectangle. CED is an equilateral triangle.

AB = xcm BC = ycm

The perimeter of ABCED is 100 cm. The area of ABCED is Rcm²

Find the value of x for which R has its maximum value.

Explain why the maximum value of R is given by this value of x.

The region, shown shaded in the diagram, is a path.

The boundary of the path is formed by two semicircles, with the same centre O, and two straight lines.

The inner semicircle has a radius of 7 metres. The path has a width of 2 metres.

Work out the perimeter of the path. Give your answer correct to one decimal place.

The diagram shows one face of a wall. This face is in the shape of a pentagon with exactly one line of symmetry.

Omondi is going to paint this face of the wall once. He has to buy all the paint that he needs to use.

The paint in each tin of paint Omondi is going to buy will cover 16 m² of the face of the wall.

Work out the least number of tins of paint Omondi will need to buy. Show your working clearly.

Here is isosceles triangle ABC.

D is the midpoint of AC and DB = 16 cm.

Angle DAB = 65

Work out the perimeter of triangle ABC. Give your answer correct to one decimal place.

The diagram shows one face of a wall. This face is in the shape of a pentagon with exactly one line of symmetry.

Omondi is going to paint this face of the wall once. He has to buy all the paint that he needs to use.

The paint in each tin of paint Omondi is going to buy will cover 16 m² of the face of the wall.

Work out the least number of tins of paint Omondi will need to buy. Show your working clearly.

Here is isosceles triangle ABC.

D is the midpoint of AC and DB = 16 cm.

Angle DAB = 65

Work out the perimeter of triangle ABC. Give your answer correct to one decimal place.

The diagram shows a right-angled triangle.

The perimeter of the triangle is 126 cm.

Work out the area of the triangle.

The diagram shows a trapezium.

Work out the area of the trapezium.

The diagram shows a cuboid.

The volume of the cuboid is 806 cm³

Work out the value of x.

A, B and C are points on a circle with centre O.

AOC is a diameter of the circle.

AB = 8 cm BC = 15 cm

Angle ABC = 90

Work out the total area of the regions shown shaded in the diagram. Give your answer correct to 3 significant figures.

The diagram shows a rectangle ABCD and a semicircle with diameter AB where AB = 12 cm. The point E lies on DC and also on the semicircle.

Work out the area of the shaded region. Give your answer correct to 3 significant figures.

The diagram shows a square and an isosceles triangle.

The square has sides of length 6 cm. The base of the isosceles triangle is 6 cm.

The perimeter of the square is equal to the perimeter of the isosceles triangle.

The shaded shape is made by putting three of the isosceles triangles around the square as shown in the diagram below.

Work out the perimeter of the shaded shape. Show your working clearly.

A box is put on a horizontal table.

The face of the box in contact with the table is a square of side 1.5 metres. The pressure on the table due to the box is 34.8 newtons/m²

The diagram shows trapezium ABCD in which BC and AD are parallel.

The trapezium has exactly one line of symmetry.

BC = 8.4 cm AD = 17.6 cm

The trapezium has area 179.4 cm²

Work out the size of angle ABC. Give your answer correct to 1 decimal place.

The diagram shows rectangle ABCD with rectangle EFGH cut out to form the shaded region.

AD = 8.3 cm correct to one decimal place DC = 7.2 cm correct to one decimal place EH = 6.2 cm correct to one decimal place HG = 5.3 cm correct to one decimal place

Work out the upper bound of the area of the shaded region. Show your working clearly.

The diagram shows a regular octagon ABCDEFGH.

Each side of the octagon has length 10 cm.

Find the area of the shaded region ACDEH. Give your answer correct to the nearest cm²

The diagram shows a quadrilateral ABCD drawn on a square grid.

Measure the length of BC.

Write down the mathematical name of quadrilateral ABCD.

Write down the order of rotational symmetry of quadrilateral ABCD.

On the diagram, mark an obtuse angle with the letter x.

Here is a diagram of a trapezium.

Work out the area of the trapezium.

The diagram shows the plan of Sophia’s gym floor.

Sophia is going to paint all the gym floor.

Each tin of paint she is going to use covers an area of 20 m²

There is a special offer on the paint that Sophia is going to buy.

Work out the least amount of money that Sophia has to pay in order to buy all the paint she needs. Show your working clearly.

The diagram shows an isosceles triangle.

Work out the area of the triangle.

The diagram shows an isosceles triangle.

Work out the area of the triangle.

Here is a rectangle.

The area of the rectangle is 28 cm²

Three of these rectangles are used to make the shape below.

Work out the perimeter of the shape.

The diagram shows a shape.

The shape has area 129 cm²

Work out the value of x.

The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ.

The perimeter of the hexagon is equal to the perimeter of the triangle.

Find the length of each side of the hexagon. Show clear algebraic working.

The diagram shows a shape.

The shape has area 129 cm²

Work out the value of x.

The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ.

The perimeter of the hexagon is equal to the perimeter of the triangle.

Find the length of each side of the hexagon. Show clear algebraic working.

The diagram shows a solid cube. The cube is placed on a table so that the whole of one face of the cube is in contact with the table.

The cube exerts a force of 56 newtons on the table. The pressure on the table due to the cube is 0.14 newtons/cm²

Work out the volume of the cube.

The diagram shows parallelogram EFGH.

EF = 9.3 cm FG = 14.7 cm Angle EFG = 106°

Work out the area of the parallelogram. Give your answer correct to 3 significant figures.

Work out the length of the diagonal EG of the parallelogram. Give your answer correct to 3 significant figures.

Here is a rectangle made from 12 square tiles.

The perimeter of each tile is 20 cm.

Work out the area of the rectangle.

The diagram shows a box in the shape of a cuboid.

The box is put on a table. The face of the box in contact with the table has length 1.2 metres and width x metres.

The force exerted by the box on the table is 27 newtons. The pressure on the table due to the box is 30 newtons/m²

Work out the value of x.

The diagram shows a shaded shape ABCD made from a semicircle ABC and a right‑angled triangle ACD.

AC is the diameter of the semicircle ABC.

Work out the perimeter of the shaded shape. Give your answer correct to 3 significant figures.

The diagram shows a prism ABCDEFGH in which ABCD is a trapezium with BC parallel to AD and CDEF is a rectangle.

BC = 7 cm AD = 12 cm DE = 10 cm

The height of trapezium ABCD is hcm The volume of the prism is 608 cm³

Work out the value of h.

L₁ and L₂ are two straight lines. The origin of the coordinate axes is O.

L₁ has equation 5x + 10y = 8 L₂ is perpendicular to L₁ and passes through the point with coordinates (8, 6) L₂ crosses the x-axis at the point A. L₂ intersects the straight line with equation x = –3 at the point B. Find the area of triangle AOB. Show your working clearly.

The diagram shows a shape made from a right-angled triangle and a semicircle.

AC is the diameter of the semicircle. BA = BC = 6 cm Angle ABC = 90°

Work out the area of the shape. Give your answer correct to 1 decimal place.

The diagram shows isosceles triangle ABC.

AB = AC = 7.5 cm. The height of the triangle is 6 cm.

Calculate the area of the triangle.

The diagram shows a shape made from a right-angled triangle and a semicircle.

AC is the diameter of the semicircle. BA = BC = 6 cm Angle ABC = 90°

Work out the area of the shape. Give your answer correct to 1 decimal place.

12

A box, in the shape of a cuboid, is going to be put on a table.

The whole of one face of the box will be in contact with the table. The force exerted by the box on the table is always 105 newtons.

The box is 5 m by 4 m by 3 m.

The greatest pressure exerted by the box on the table is P newtons/m² The least pressure exerted by the box on the table is Q newtons/m²

Work out the value of PQ

ABCD is a trapezium.

21.2 cm C

Calculate the perimeter of the trapezium. Give your answer correct to 3 significant figures.

Here is a hexagon ABCDEF.

CD is parallel to AF.

Work out the area of hexagon ABCDEF.

The diagram shows a right-angled triangle.

Five of these triangles are put together to make a shape.

The diagram shows a quadrilateral ABCD on a centimetre grid.

Work out the area of triangle ABC. You must include the units with your answer.

Give a reason why angle ACD is equal to angle CAB.

Write down an equation for the straight line that passes through D and C.