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Lesson 6 of 12

Area of a triangle

I can derive the formula for the area of a triangle.

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Lesson 6 of 12
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Area of a triangle

I can derive the formula for the area of a triangle.

Lesson details

Key learning points

  1. It is possible to find a relationship between triangles and parallelograms.
  2. You can use this relationship to find a formula for the area of a triangle.
  3. It is possible to identify the base and perpendicular height of any triangle even when they are not obvious.
  4. The formula can be used to find the area of any triangle.

Keywords

  • Base - The base is the side which is perpendicular to the height.

  • Perpendicular height - The perpendicular height is the perpendicular distance from the base to the opposite vertex.

Common misconception

Pupils may forget to halve after multiplying the base and the perpendicular height.

The area of a triangle is equal to half the area of the parallelogram formed by two of those triangles.

Ensure pupils have the opportunity to cut out and physically mainpulate the trianges to form different quadrilaterals and have them discuss as a class which quadrilateral they could all make.
Teacher tip

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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Prior knowledge starter quiz

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6 Questions

Q1.
What type of shape is this?

An image in a quiz
equilateral triangle
isosceles triangle
Correct answer: right-angle triangle
scalene triangle

Q2.
What type of shape is this?

An image in a quiz
Correct answer: equilateral triangle
isosceles triangle
right-angle triangle
scalene triangle

Q3.
What type of shape is this?

An image in a quiz
equilateral triangle
isosceles triangle
right-angle triangle
Correct answer: scalene triangle

Q4.
What type of shape is this?

An image in a quiz
equilateral triangle
Correct answer: isosceles triangle
right-angle triangle
scalene triangle

Q5.
True or false? In order to calculate the area of a shape, you sum the side lengths of the shape.

True
Correct answer: False

Q6.
The angles in a triangle sum to

Correct Answer: 180 degrees, 180

Assessment exit quiz

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6 Questions

Q1.
The perpendicular height is the perpendicular distance from the to the opposite vertex.

Correct Answer: base

Q2.
True or false? You can calculate the area of this triangle.

An image in a quiz
True
Correct answer: False

Q3.
True or false? You can calculate the area of this triangle.

An image in a quiz
True
Correct answer: False

Q4.
Calculate the area of a triangle with a base of 8 cm and a perpendicular height of 5 cm (you do not need to give the units).

Correct Answer: 20, Twenty

Q5.
Two identical triangles can always be placed together to create a

Correct Answer: parallelogram

Q6.
Which of these is not a way to calculate the area of this triangle?

An image in a quiz
Correct answer: base $$\times$$ perpendicular height $$\times$$ 0.2
base $$\times$$ perpendicular height $$\times {1 \over 2}$$
$$b \times h \times {1 \over 2}$$
$$bh \over 2$$

Lesson appears in

UnitMaths / Perimeter and area

Maths

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