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Area (F) - Questions

Q1.

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

Work out the total area of the shape.

........................................................... cm2

(Total for question = 3 marks)

Q2.

The diagram shows a square ABCD of side 8 cm inside a circle, centre O. The vertices of the square lie on the circle.

Work out the total area of the four shaded segments.

Give your answer correct to 3 significant figures.

........................................................... cm2


Q3.

A is in the shape of a quarter circle of radius 15 cm. B is in the shape of a circle.

The area of A is 9 times the area of B.

Show that the radius of B is 2.5 cm.


Q4.

........................................................... m2


Q5.

* The diagram shows the floor plan of Mary's conservatory.

Mary is going to cover the floor with tiles.

The tiles are sold in packs. One pack of tiles will cover 2m2

A pack of tiles normally costs £24.80 Mary gets a discount of 25% off the cost of the tiles.

Mary has £100

Does Mary have enough money to buy all the tiles she needs? You must show all your working.


Q6.

Here are two rectangles.

All measurements are in centimetres.

The area of rectangle A is equal to the area of rectangle B.

Work out the perimeter of rectangle B.

........................................................... cm


Q7.

Here is a star shape.

The star shape is made from a regular hexagon and six congruent equilateral triangles.

The area of the star shape is 96 cm2.

Work out the area of the regular hexagon.

........................................................... cm2


Q8.

Here is a shaded shape on a grid of centimetre squares.

(a) Find the perimeter of the shaded shape.

..............................................................................................................................................(1)

(b) Find the area of the shaded shape.

. . . . . . . . . . . . . . . . . . . . cm2

(1)(c) Reflect the shaded shape in the mirror line.

(2)(Total for Question is 4 marks)

Q9.

ABDE is a rectangle. ED is 8cm.

BDC is a right-angled triangle. BC is 4.5cm.

ABC is a straight line.

The area of the rectangle ABDE is 40cm2. Work out the area of the triangle BDC.

...........................................................cm2


Q10.


Q11.

Here is a shape. All the measurements are in metres.

The area of the shape is A m2.

Find a formula for A in terms of x.

......................................................................................................................


Q12.

(a) On the grid, draw an isosceles triangle.

(1)(b) On the grid, draw a rectangle with an area of 12 cm2.

(2)

(Total for Question is 3 marks)

Q13.

Balena has a garden in the shape of a circle of radius 10 m. He is going to cover the garden with grass seed to make a lawn.

Grass seed is sold in boxes. Each box of grass seed will cover 46 m2 of garden.

Balena wants to cover all the garden with grass seed.

(a) Work out an estimate for the number of boxes of grass seed Balena needs.

You must show your working.

...........................................................

(4)(b) Is your estimate for part (a) an underestimate or an overestimate?

Give a reason for your answer.

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

(1)


Q14.

This shape is made from two rectangles.

(a) Work out an estimate for the total area of the shape.

........................................................... cm2

(3)(b) Is your answer to (a) an overestimate or an underestimate?

Give a reason for your answer.

.............................................................................................................................................

.............................................................................................................................................

(1)


Q15.

The diagram shows a semicircle drawn inside a rectangle.

The semicircle has a diameter of 8 cm. The rectangle is 8 cm by 4 cm.

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

. . . . . . . . . . . . . . . . . . . . . . . . cm2


Q16.

The diagram shows a trapezium ABCD and two identical semicircles.

The centre of each semicircle is on DC.


........................................................... cm2


Q17.

ABCDE is a pentagon.

Work out the area of ABCDE.

........................................................... cm2


Q18.

The shaded shape is drawn on a grid of centimetre squares.

(a) Find the perimeter of the shaded shape.

. . . . . . . . . . . . . . . . . . . . . . cm

(1)(b) Find the area of the shaded shape.

. . . . . . . . . . . . . . . . . . . . . . cm2


Q19.

The diagram shows the plan of a floor.

The area of the floor is 138 m2.

Work out the value of x.

...........................................................


Q20.

The diagram shows a shape ABCDEF.

All the corners of the shape are right angles. The perimeter of the shape is 28 m.

Work out the area of ABCE shown shaded on the diagram.

...........................................................


Q21.

Frances grows plants in a container. Each of the 5 faces of the container is made of glass.

The container is in the shape of a prism. The cross section of the prism is an isosceles triangle with height 40 cm.

BC = 60 cm AB = AC = 50 cm CP = 80 cm

Work out the total area of glass needed to make the container.

........................................................... cm2


Q22.

Work out the area of the shape.

........................................................... cm2

(Total for question is 2 marks)

Q23.

A pattern is made using identical rectangular tiles.

Find the total area of the pattern.

........................................................... cm2


Q24.

The arc ABC is a quarter of a circle with centre O and radius 4.8 cm. AC is a chord of the circle.

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

........................................................... cm2


Q25.

The diagram shows a semicircle drawn inside a rectangle.

The semicircle has a diameter of 8 cm. The rectangle is 8 cm by 4 cm.


. . . . . . . . . . . . . . . . . . . . . . . . cm2


Q26.

Peter has 4 photos. Each photo is in the shape of a rectangle with dimensions 12 cm by 8 cm.

Peter is going to enlarge each photo by a scale factor of 1.5 He wants to put all 4 enlarged photos in the picture frame shown below.

The dimensions of the outside of the picture frame are 40 cm by 26 cm. The width of each side of the frame is 2 cm.

Can the 4 enlarged photos be put in the picture frame so they do not overlap? You must show how you get your answer.


Q27.

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.


Q28.

The diagram shows a rectangular garden path.

Wasim is going to cover the path with paving stones. Each paving stone is a square of side 30 cm. Each paving stone costs £2.50

Wasim has £220 to spend on paving stones.

Show that he has enough money to buy all the paving stones he needs.


Q29.

Here are two rectangles.

QR = 10 cm BC = PQ

The perimeter of ABCD is 26 cm The area of PQRS is 45 cm2

Find the length of AB.

........................................................... cm


Q30.

* The diagram shows the plan of a floor.

Angie is going to varnish the floor.

She needs 1 litre of varnish for 5 m2 of floor. There are 2.5 litres of varnish in each tin of varnish.

Angie has 3 tins of varnish.

Does she have enough varnish for all the floor? You must show all your working.


Q31.

A square has an area of 81 cm2

(a) Find the perimeter of the square.

........................................................... cm

(2)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.

(b) Find the value of h.

h = ...........................................................

(3)


Q32.

A tin of varnish costs £15

A rectangular floor has dimensions 6 m by 11 m. The floor is going to be covered in varnish.

Helen assumes that each tin of this varnish covers an area of 12 m2.

(a) Using Helen's assumption, work out the cost of buying the varnish for this floor.

£ ...........................................................

(4)Helen finds that each tin of varnish covers less than 12 m2.

(b) Explain how this might affect the number of tins she needs to buy.

.............................................................................................................................................

.............................................................................................................................................

(1)


Q33.

James has some square paving stones and some rectangular paving stones.

He uses four square paving stones and six rectangular paving stones to make this pattern in the shape of a rectangle.

Each rectangular paving stone is 60 cm by 30 cm.

(a) Work out the length of one side of a square paving stone.

........................................................... cm

(2)Sally is going to make a path with rectangular paving stones. Each paving stone is 60 cm by 30 cm.

The path will be 720 cm long and 120 cm wide.

(b) Work out how many paving stones Sally needs to make the path.

...........................................................

(3)


Q34.

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

Karen is going to cover this part of the wall with tiles. Each rectangular tile is 15 cm by 7.5 cm

Tiles are sold in packs. There are 9 tiles in each pack.

Karen divides the area of the wall by the area of a tile to work out an estimate for the number of tiles she needs to buy.

(a) Use Karen's method to work out an estimate for the number of packs of tiles she needs to buy.

...........................................................

(5)

Karen is advised to buy 10% more tiles than she estimated. Buying 10% more tiles will affect the number of the tiles Karen needs to buy.

She assumes she will need to buy 10% more packs of tiles.

(b) Is Karen's assumption correct? You must show your working.

(2)


Q35.

* Here is a diagram of a wall.

Halima wants to cover all of the wall with tiles.

The tiles are squares with sides of length 20 cm.

The tiles are sold in packs. There are 10 tiles in each pack. Each pack of tiles costs £34.99

Halima only has £1000

Can she buy enough packs of tiles to cover the wall?


Q36.

* The diagram shows the floor plan of Jill's dining room.

Jill is going to cover the floor with wooden floorboards.

The floorboards are sold in packs. One pack of floorboards will cover 2.25 m2.

Work out how many packs Jill needs. You must show all your working.


Q37.

The diagram shows a patio in the shape of a rectangle.

The patio is 3.6 m long and 3 m wide.

Matthew is going to cover the patio with paving slabs.Each paving slab is a square of side 60 cm.

Matthew buys 32 of the paving slabs.

(a) Does Matthew buy enough paving slabs to cover the patio?

You must show all your working.

. . . . . . . . . . . . . . . . . . . . . .

(3)The paving slabs cost £8.63 each.

(b) Work out the total cost of the 32 paving slabs.

£ . . . . . . . . . . . . . . . . . . . . . .


Q38.

Shirley has a garage.

Here is a plan of her garage floor.

Shirley wants to buy enough paint to cover the garage floor as cheaply as possible. She can buy her paint from Decor U or from Paint Store.

From which of these two shops should Shirley buy her paint?



Q39.

Jake is going to make a path from small paving stones and large paving stones. The diagram shows Jake's design for the path. The rest of the path is made using the same pattern of paving stones.

A small paving stone costs £2.30 A large paving stone costs £3.65

Jake needs to buy enough paving stones to make a path that is 6 metres long.

(a) How much will Jake have to pay for the paving stones he needs?

£ ...........................................................

(4)Harry designs a different path that is also 6 metres long using the large paving stones.

Harry says that the cost of his path will be less than half of the cost of the path that Jake designed.

(b) Is Harry correct?

You must show how you get your answer.

(2)


Q40.Here is a diagram of a small field.

All the corners are right angles.

90% of the field is going to be used to grow wheat.

Work out the area of the field that is going to be used to grow wheat.

........................................................... m2


Q41.

Here is a diagram showing a rectangle, ABCD, and a circle.

BC is a diameter of the circle.

Calculate the percentage of the area of the rectangle that is shaded. Give your answer correct to 1 decimal place.

...........................................................%


Q42.

An equilateral triangle has sides of length 8 cm. A square has the same perimeter as the triangle.

Work out the area of the square.

...........................................................


Q43.

A garden is in the shape of a rectangle, ABCD, and a semicircle. AD is the diameter of the semicircle.

Carol is going to cover the garden with fertiliser.

A box of fertiliser costs £4.99 Carol has been told that one box of fertiliser will cover 12 m2 of garden.

(a) Work out the cost of buying enough fertiliser to cover the garden completely.

£ ...........................................................

(5)Carol finds out that one box of fertiliser will cover more than 12 m2 of garden.

(b) Explain how this might affect the number of boxes she needs to buy.

.............................................................................................................................................

.............................................................................................................................................

(1)


Q44.

* The diagram shows the surface of a pond in the shape of a circle.

The circle has a radius of 120 cm.

Mark wants to put 20 fish into the pond. There needs to be a surface area of 1800 cm2 for each fish.

Show that the surface of the pond is large enough for Mark to put 20 fish into the pond.


Q45. ∗The diagram shows the plan of a small field.

Kevin is going to keep some pigs in the field. Each pig needs an area of 36 square metres.

Work out the greatest number of pigs Kevin can keep in the field.


Q46.

The diagram shows a garden with 4 flower beds. The garden is a rectangle, 23 m by 17 m.

Diagram NOT accurately drawn

Each flower bed is a rectangle with the same length and the same width.

Work out the length and the width of a flower bed.

length =...........................................................m

width =...........................................................m


Q47.

The diagram shows a rectangular floor.

Toji is going to cover the floor with floor boards. Each floor board is 0.1 m wide and 1.5 m long.

Work out the smallest number of floor boards Toji needs.

...........................................................


Q48.

*Here is a diagram of a garden.

The lawn is a 6 m by 4 m rectangle. Sabia is going to put a path all the way around the lawn. The path will be 0.5 m wide.

Sabia is going to use paving stones to make the path. Each paving stone is a 0.5 m by 0.5 m square. She has 35 paving stones.

Has Sabia got enough paving stones? You must show all your working.


Q49.

Here are a triangle and a rectangle.

The area of the rectangle is 6 times the area of the triangle.

Work out the width of the rectangle.

........................................................... cm


Q50.

The diagram shows a shape made by overlapping two identical squares.

The area of the shaded region is 25% of the area of each square.

Work out what fraction of the area of the whole shape is shaded.

...........................................................


Q51.

The diagram shows a square ABCD inside a circle.

The points A, B, C and D lie on the circle.

The radius of the circle is 6 cm.

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

........................................................... cm2


Q52.

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.


Q53.

The diagram shows a path around a pond.

The pond is in the shape of a rectangle with length 7 m and width 4 m. The path is 3 m wide.

Ali is going to cover the path with gravel. One bag of gravel will cover 10 m2 of the path.

How many bags of gravel does Ali need to buy? You must show your working.

........................................................... bags


Q54.

Here is a diagram of part of a wall in Sarah's house.

Sarah is going to cover this part of the wall with square tiles. The square tiles have sides of 20 cm.

Work out the number of tiles Sarah needs.

..............................................................................................................................................(Total for Question is 3 marks)

Q55.

A square of side 3 cm is made from nine squares of side 1 cm.

(a) How many more squares of side 1 cm are needed to make a square of side 6 cm?

...........................................................(2)

Here is a tile.

Here is a sequence of patterns made from these tiles.

(b) How many of these tiles are needed to make Pattern number 7?

...........................................................(2)


Q56.

The diagram shows a square with perimeter 16 cm.

Work out the proportion of the area inside the square that is shaded.

...........................................................


Q57.

* Mr Weaver's garden is in the shape of a rectangle.

In the gardenthere is a patio in the shape of a rectangleand two ponds in the shape of circles with diameter 3.8 m.

The rest of the garden is grass.

Mr Weaver is going to spread fertiliser over all the grass.One box of fertiliser will cover 25 m2 of grass.

How many boxes of fertiliser does Mr Weaver need?You must show your working.


Q58.

The diagram shows a logo made from three circles.

Each circle has centre O.

Daisy says that exactly of the logo is shaded.

Is Daisy correct? You must show all your working.


Q59.

Andy is going to cover a wall with tiles.

The wall is in the shape of a rectangle. The wall is 3 m wide and 2.5 m high. The tiles are rectangles 20 cm wide and 25 cm high.

The tiles are sold in boxes. There are 20 tiles in each box. Each box of tiles costs £8.50

Work out the total cost of the boxes of tiles Andy needs to buy. You must show all your working.

£ ...........................................................


Q60.

* The diagram shows the floor of a village hall.

The caretaker needs to polish the floor.

One tin of polish normally costs £19

One tin of polish covers 12 m2 of floor.

There is a discount of 30% off the cost of the polish.

The caretaker has £130

Has the caretaker got enough money to buy the polish for the floor?



Q61.

Here is a rectangle.

The length of the rectangle is 7 cm longer than the width of the rectangle.

4 of these rectangles are used to make this 8-sided shape.

The perimeter of the 8-sided shape is 70 cm.

Work out the area of the 8-sided shape.

........................................................... cm2


Q62.

The diagram shows a rectangular wall.

Frank is going to cover the wall with rectangular tiles. Each tile is 60 cm by 30 cm.

of the tiles will be white.

Some of the tiles will be green. The rest of the tiles will be blue.

The ratio of the number of green tiles to the number of blue tiles will be 1 : 3

(a) Assuming there are no gaps between the tiles, how many tiles of each colour will Frank need?

white tiles ...........................................................

green tiles ...........................................................

blue tiles ...........................................................

(5)Frank is told that he should leave gaps between the tiles.

(b) If Frank leaves gaps between the tiles, how could this affect the number of tiles he needs?

.............................................................................................................................................

.............................................................................................................................................

(1)


Q63.

Here is a diagram of Jim's garden.

Jim wants to cover his garden with grass seed to make a lawn.

Grass seed is sold in bags.There is enough grass seed in each bag to cover 20 m2 of garden.

Each bag of grass seed costs £4.99

Work out the least cost of putting grass seed on Jim's garden.

£...........................................................


Q64.

* The diagram shows the plan of the floor of Mrs Phillips' living room.

Mrs Phillips is going to cover the floor with floor boards.One pack of floor boards will cover 2.5 m2.

How many packs of floor boards does she need?You must show your working.


Q65.

Jade wants to paint a wall.

The paint is sold in three sizes of tin.

The table gives information about the tins of paint.

Size of tin Cost

1 litre £6 3 litres £15 5 litres £23.50

1 litre of this paint covers an area of 8 m2. The wall has an area of 112 m2.

Work out the cheapest cost of the paint Jade needs.

..............................................................................................................................................(Total for Question is 4 marks)

Q66.

Here is a right-angled triangle.

The shape below is made from 4 of these triangles.

(a) Work out the area of the shape.

. . . . . . . . . . . . . . . . . . . . . . cm2

(3)(b) Work out the perimeter of the shape.

..............................................................................................................................................(3)


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