Robinson Tuition
Grade 3 · Foundation · free GCSE maths worksheet

Area of triangles and parallelograms

Base times height formulae.

22 original questions, 76 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

A parallelogram has a base of 9 cm and a perpendicular height of 6 cm.

Work out the area of the parallelogram.

2 marks
Show answer
54 cm2
2

A triangle has a base of 12 cm and a perpendicular height of 7 cm.

Work out the area of the triangle.

2 marks
Show answer
42 cm2
3

A rectangle has length 9 cm and width 4 cm.

  1. Work out the area of the rectangle.
  2. Work out the perimeter of the rectangle.
2 marks
Show answer
a) 36 cm2 b) 26 cm
4

A triangle has base 12 cm and perpendicular height 5 cm.

Work out the area of the triangle.

2 marks
Show answer
30 cm²
5

Ben wants to work out the perimeter of a square with sides of length 6 cm.

Ben writes:

perimeter = 6 × 6 = 36 cm

Explain the mistake Ben has made.

2 marks
Show answer
6 x 6 gives the area of the square, not the perimeter. The perimeter is 4 x 6 = 24 cm.
6

The diagram shows a shape drawn on a centimetre square grid. Each square has sides of 1 cm.

  1. Work out the area of the shape.
  2. Work out the perimeter of the shape.
3 marks
Show answer
a) 18 cm² b) 20 cm
7

A square has an area of 81 cm2.

An equilateral triangle has the same perimeter as the square.

Work out the length of one side of the triangle.

3 marks
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12 cm
8

The front of a shed is made from a rectangle with a triangle on top.

The rectangle is 10 cm wide and 6 cm high in a scale drawing. The triangle sits exactly on top of the rectangle, with base 10 cm and perpendicular height 4 cm.

Work out the total area of the scale drawing.

10 cm6 cm4 cmDiagram NOT accurately drawn
4 marks
Show answer
80 cm²
9

A parallelogram has an area of 72 cm².

Its base is 12 cm.

Work out the perpendicular height of the parallelogram.

3 marks
Show answer
6 cm
10

A triangle has an area of 30 cm².

Its base is 12 cm.

Work out the perpendicular height of the triangle.

3 marks
Show answer
5 cm
11

Rectangle A has length 12 cm and width 5 cm.

Rectangle B has width 4 cm. The perimeter of rectangle B is equal to the perimeter of rectangle A.

Work out the area of rectangle B.

4 marks
Show answer
52 cm²
12

A rectangular patio is 4.5 m long and 3.6 m wide.

The patio is to be covered completely with square paving slabs. Each slab has sides of length 0.9 m and costs £7.25.

Work out the total cost of the slabs needed. You may assume no slabs are cut.

4 marks
Show answer
£145
13

The diagram shows a trapezium drawn on a centimetre square grid. Each square has sides of 1 cm.

On the grid, draw a triangle that has the same area as the trapezium. The corners of your triangle must be on grid points.

3 marks
Show answer
Any triangle with area 6 cm2 with corners on grid points, for example base 4 cm and height 3 cm
14

The diagram shows the line AB on a centimetre square grid. Each square has sides of 1 cm.

AB is the base of triangle ABC. The area of triangle ABC is 12 cm².

On the grid, mark the point C and complete the triangle ABC.

AB
2 marks
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Point C 6 cm above line AB, for example at (4, 8)
15

A square has an area of 64 cm².

A rectangle has the same perimeter as the square.

The width of the rectangle is 5 cm.

Work out the area of the rectangle.

4 marks
Show answer
55 cm2
16

A triangle has base (x + 4) cm and perpendicular height 6 cm.

The area of the triangle is 42 cm².

  1. Show that 3x + 12 = 42.
  2. Work out the value of x.
4 marks
Show answer
a) area = 1/2 x 6 x (x + 4) = 3(x + 4) = 3x + 12, and this equals 42 b) 10
17

Layla is paving a rectangular patio 6 m long and 4 m wide.

Each paving slab is a square of side 50 cm and costs £3.80.

Layla has a budget of £400.

Does she have enough money? You must show your working.

4 marks
Show answer
Yes, the slabs cost £364.80
18

The end wall of a barn is a trapezium. The parallel sides of the trapezium are 6 m and 8 m long, and the perpendicular distance between them is 3 m.

Priya is going to paint the wall. One tin of paint covers 5 m² and costs £13.50.

Work out the total cost of the tins of paint Priya needs to buy.

5 marks
Show answer
£67.50
19

An isosceles trapezium has parallel sides of 4 cm and 16 cm.

Its two sloping sides are each 10 cm long.

Its area is 80 cm².

  1. Work out the perpendicular height of the trapezium.
  2. Work out the perimeter of the trapezium.
4 marks
Show answer
a) 8 cm b) 40 cm
20

Rectangle P has length 20 cm and width x cm.

Square Q has sides of length 8 cm.

The area of rectangle P is twice the area of square Q.

Work out the perimeter of rectangle P.

5 marks
Show answer
52.8 cm
21

A row of 6 identical square tiles has a length of 90 cm.

A wall is 2.4 m wide and 1.5 m high.

Tiles are used to cover the whole wall with no gaps.

How many tiles are needed?

4 marks
Show answer
160
22

Jade is tiling a wall in the shape of a trapezium. The parallel sides of the wall are 3 m and 5 m long, and the perpendicular distance between them is 2.4 m.

Each tile is a square with sides of length 30 cm. Tiles are sold in packs of 12. Each pack costs £18.

  1. Work out the total cost of the packs of tiles Jade needs to buy. You may assume no tiles are wasted.
  2. Jade decides to allow 10% extra tiles for cutting and breakage. Does this change the number of packs she needs to buy? You must show your working.
7 marks
Show answer
a) £162 b) yes, 10 packs are now needed instead of 9

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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