Area & Perimeter (AQA GCSE Maths: Higher): Exam Questions

The diagram shows a triangle.

In the diagram, all the measurements are in metres.

The perimeter of the triangle is 56 m.
The area of the triangle is A m².

Work out the value of A.

The diagram shows 3 identical circles inside a rectangle.
Each circle touches the other two circles and the sides of the rectangle, as shown in the diagram.

The radius of each circle is 24 mm.

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

Here is a right-angled triangle.

Four of these triangles are joined to enclose the square  as shown below.

Show that the area of the square  .

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.

and  are straight lines.
Angle  = Angle 

Work out the area of the trapezium .

Work out the length of .

 is an isosceles triangle.

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

Here is a parallelogram.

Angle  is 

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

The diagram shows a triangle  inside a rectangle .

Show that the area of triangle  is 8 cm².
You must show all your working.

and  are straight lines.  is parallel to .

Angle 

is the midpoint of .

Work out the area of trapezium .

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.

The diagram shows a square with perimeter 16 cm.

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

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?
You must show all your working.

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.

Rectangle is split into four smaller rectangles.
Two of the smaller rectangles are shaded.

For rectangle , work out the ratio shaded area : unshaded area

Give your answer in its simplest form.

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.

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

The diagram shows a rectangle and a semicircle with diameter where . The point lies on 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 shape.

The shape has area 
Work out the value of .

is a square with a side length of 
is the midpoint of .
is the point on  where

 is a right-angled triangle.

Find an expression, in terms of , for the area of triangle . Give your expression in its simplest form.

The line  is a tangent to the circle  at the point .
is the point (2, 6).

The line  crosses the -axis at the point .

Work out the area of triangle .

Here is an L-shape.

All dimensions are in centimetres.

The area of the L-shape is 65 cm²

Work out the value of.

Here is a right-angled triangle.

All measurements are in centimetres.
The area of the triangle is 2.5 cm².

Find the perimeter of the triangle.
Give your answer correct to 3 significant figures.
You must show all of your working.

Figure 2

The line , shown in Figure 2 has equation 2 + 3 = 26.
The line passes through the origin  and is perpendicular to .
Find an equation for the line .

The line intersects the line at the point .
Line crosses the y-axis at the point as shown in Figure 2.

Find the area of triangle .

Give your answer in the form , where and are integers to be determined.

The diagram shows a logo.

and are congruent triangles.
is a sector of a circle, centre .

Show that the area of the logo is 510 cm² to 2 significant figures.

The diagram shows a shaded region formed by removing an equilateral trianglefrom a regular hexagon .

The points and lie on such that .

Given that the area of region is
work out the length of .

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

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.

The diagram shows an isosceles triangle.

The area of the triangle is 

Work out the perimeter of the triangle.

Give your answer correct to  significant figures.

   cm 

Calvin has  identical rectangular tiles.
He arranges the tiles to fit exactly round the edge of a shaded rectangle, as shown in the diagram below.

Work out the area of the shaded rectangle.

and are points on a circle with centre .

is a diameter of the circle.

Angle

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 regular octagon 

Each side of the octagon has length 

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

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

The diagram shows a circle and a trapezium.

The height of the trapezium is .

The area of the circle is equal to the area of the trapezium.

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

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

is the diameter of the semicircle .

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

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

The diagram shows two circles such that the region , shown shaded in the diagram, is the region common to both circles.

One of the circles has centre and radius 5cm.
The other circle has centre and radius 4 cm.
Angle

Calculate the area of region .
Give your answer correct to 3 significant figures.

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

The diagram shows Jane’s lawn.
It is in the shape of a square of side 36m and three semi-circles.

She is going to spread fertiliser on the lawn at a rate of 30g per square metre.
The fertiliser is only sold in 10kg bags costing £15.80 each.

Calculate the cost of buying the bags of fertiliser for her lawn.
You must show all your working.

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

ABCD is a trapezium.

The perimeter of the trapezium is 56 cm.
The ratio AD : AB : DC : BC = 5 : 12 : 6 : 5.

Calculate the area of the trapezium.
Show your working.

..................................cm²

In the diagram, the square and the trapezium share a common side of length x cm.

The area of the square is equal to the area of the trapezium.

Work out the value of x.

x = .................. 

Here is the floor plan of a rectangular room.

Tim buys carpet tiles for this room.

Each tile is a square measuring 50cm by 50cm.
The tiles are only sold in packs of ten.
Each pack costs £20.
Tim pays for fitting at a rate of £7.50 per square metre, with any fraction of a square metre rounded up.

Work out the total cost of the tiles and fitting.

£ ..........................

The lengths of the sides of two squares are integers, when measured in cm.
The difference between the areas of the two squares is 36cm².

Find the lengths of the sides of the two squares.

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