Area & Perimeter (Edexcel GCSE Maths: Foundation): Exam Questions

The length, $l$, of a rectangle is 3 cm longer than the width, $w$.
The perimeter of the rectangle is 26 cm.

Calculate the length, $l$, and the width, $w$.

$\begin{array}{l}l=....................................\mathrm{cm}\\ w=...................................\mathrm{cm}\end{array}$ 

The diagram shows the plan of part of Rachel’s garden.

Calculate the area.

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

Calculate the area of the trapezium.

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

Find an expression for the perimeter of this triangle.
Give your answer in its simplest form.

The diagram shows a rectangular patio with sides 6m and 8m.

i) Work out the perimeter of the patio.

............................................. m [1]

ii) Henri covers the patio floor with square tiles.
The tiles are 0.5m by 0.5m.

Work out the number of tiles he needs.

[2]

The diagram shows the floor of a room.

i) Calculate the area of the floor.

............................................... m² [2]

ii) Henry buys varnish for the floor of the room.
500ml of varnish covers 8m² of floor.

Calculate the amount of varnish Henry needs.

............................................... ml [2]

The diagram shows one wall of the room.

Calculate the area of the wall.

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

The diagram shows a shape made from two rectangles.

i) Work out the perimeter.

.............................................. cm [2]

ii) Work out the area.

............................................. cm² [2]

The scale drawing shows a play area, $ABCDE$.
The scale is 1 centimetre represents 3 metres.

Find the actual distance $h$ in metres.

$h=$ .............................m 

Find the actual area of triangle $CDE$.

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

Calculate the area of this trapezium.

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

Find an estimate for the area of the shape drawn on this 1 cm² grid.

............................... cm² 

Here is a triangle and a rectangle.

The base of the triangle is 6 cm.

The height of the triangle is the same as the length of the rectangle.

The width of the rectangle is 3 cm.

The perimeter of the rectangle is 36 cm.

Work out the area of the triangle.

The diagram shows 12 identical grey rectangles inside a large rectangle.

The length of the large rectangle is 24 cm.

The length of a grey rectangle is twice its width.

Work out the width of the large rectangle.

Edwin's back garden is in the shape of a rectangle, with dimensions 11 metres by 5 metres.

Edwin wants to cover the garden with artificial grass.

Each section of artificial grass is rectangular in shape.
Each section is 1.25 metres long and 1 metre wide.

Edwin has 40 sections of artificial grass.
Does he have enough artificial grass to cover his back garden?
You must show how you get your answer.

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

Sandra is going to paint the floor.

Each 4 litre tin of paint costs £21.99.

1 litre of paint covers an area of 2m².

Sandra has £50 to spend on paint.

Has Sandra got enough money to buy all the paint she needs?

You must show how you get your answer.

Work out the area of the shape.

Below are two circles.

$PQR$ is a straight line.

This diagram is not to scale.

$PQ$ is the diameter of the larger circle.

$QR$ is the diameter of the smaller circle.

The length $PQ$ is four times the length $QR$.

$PR=70\mathrm{cm}$

Work out the length of $PQ$.

Work out the area of the smaller circle.

Give your answer to 2 decimal places.

Include units in your answer.

Work out the circumference of the larger circle.

Give your answer in terms of $\mathrm{\pi }$.

Give an example to show that when a piece is cut off a square the perimeter of the new shape

(i) is less than the perimeter of the square,

(ii) is the same as the perimeter of the square,

(iii) is greater than the perimeter of the square.

Jerry draws a rectangle with an area of 24 cm².

One side length is 7.5 cm.

Calculate the perimeter of the rectangle.

Write your answer in centimetres.

The pathway in Alan's garden is made up of identical paving slabs.

Find the total area of the pathway.

The area of triangle $ABC$ is 27 cm² and $AB$ = 6 cm.

Calculate the value of $h$.

$h$ = ................................................. 

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

Pip is going to cover this part of the patio with tiles.
Each tile is rectangular, 12 cm by 8 cm.

Tiles are sold in packs.
There are 15 tiles in each pack.

Pip divides the area of this patio by the area of a tile to work out an estimate for the number of tiles she needs to buy.

Use Pip's method to work out the estimate for the number of packs of tiles she needs to buy.

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

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

Is Pip's assumption correct?

You must show your working.

The area of the parallelogram is the same as the area of the trapezium.

Work out the value of $x$.

$x$= ................................................ 

Rectangle$A$measures 3 cm by 8 cm.

Five rectangles congruent to $A$ are joined to make a shape.

Work out the perimeter of this shape.

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

A square has perimeter 12$x$.

Find an expression, in terms of $x$, for the area of the square.
Give your answer in its simplest form.

The diagram shows a semicircle with diameter$AC$.
B is a point on the circumference and $AB=BC$.

Work out the area of triangle $ABC$.

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

The diagram shows a right-angled triangle.

Calculate the perimeter.

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

The diagram shows the front of Pranav’s house.

i) Work out the total area of the front of his house.

............................................ m² [3]

ii) The door is 0.9 m wide and 2.1 m high.
Each of the four windows are 1.5 m wide and 1.2 m high.

Work out the total area of the door and the four windows.

............................................ m² [3]

iii) Pranav paints the front of his house but not the door and not the four windows.

Work out the area he paints.

............................................ m² [1]

The area of this triangle is 363cm².

Calculate the value of $h$.

$h=$ ..............................