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Year 7

Area of a trapezium

I can derive and use the formula for the area of a trapezium.

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New
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Year 7

Area of a trapezium

I can derive and use the formula for the area of a trapezium.

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Share activities with pupils
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Lesson details

Key learning points

  1. The area of some trapezia can be found by using compound shapes.
  2. It is possible to find a relationship between trapizea and parallelograms.
  3. The relationship between parallelograms and trapezia can be used to deduce the formula for the area of a trapezium.
  4. The formula can be used to calculate the area of a trapezium.

Keywords

  • Trapezium - A trapezium is a quadrilateral with a pair of parallel opposite sides.

  • Trapezia/trapeziums - The plural of trapezium can be referred to as trapezia or trapeziums.

Common misconception

Pupils may incorrectly identify the base of the triangle in the trapezium.

Drawing a trapezium on paper, colouring the sides and cutting it will help them see where the base of the triangle comes from.

There is a lot of suggested drawing in this lesson and pupils may benefit from using mini whiteboards for this as they allow pupils to quickly edit their drawings and easily share ideas between them
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Licence

This content is © Oak National Academy Limited (2025), licensed on

Open Government Licence version 3.0
except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
The perpendicular height is the perpendicular from the base to the opposite vertex.
Correct Answer: distance, length
Q2.
Calculate the area of a triangle with a base of 12 cm and a perpendicular height of 15 cm.
Correct answer: 90 cm$$^2$$
180 cm$$^2$$
13.5 cm
27 cm
Q3.
Calculate the area of the triangle.
An image in a quiz
54 cm$$^2$$
Correct answer: 55 cm$$^2$$
60 cm$$^2$$
66 cm$$^2$$
Q4.
You can write a to calculate the area in an efficient way.
Correct Answer: formula
Q5.
Calculate the area of this compound rectilinear shape (you do not need to state the units).
An image in a quiz
Correct Answer: 5, 5 m$$^2$$
Q6.
Calculate the area of this compound rectilinear shape (you do not need to state the units).
An image in a quiz
Correct Answer: 66, 66 cm$$^2$$

Exit quiz

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6 Questions

Q1.
A trapezium is a with exactly one pair of parallel opposite sides.
Correct Answer: quadrilateral
Q2.
Any trapezium can be made using a rectangle and a
Correct Answer: triangle
Q3.
True or false? The formula for the area of a trapezium has to be written as $${1\over2} \times (a + b) \times h$$
True
Correct answer: False
Q4.
Calculate the area of the trapezium (you do not need to state the units).
An image in a quiz
Correct Answer: 12, 12 cm$$^2$$
Q5.
Calculate the area of the trapezium (you do not need to state the units).
An image in a quiz
Correct Answer: 47.5, 47.5 cm$$^2$$
Q6.
Calculate the area of the trapezium (you do not need to state the units).
An image in a quiz
Correct Answer: 80, 80 cm$$^2$$