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Using the formula for the area of a triangle

I can use the formula for the area of a triangle to calculate missing side lengths.

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Lesson 7 of 12

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Year 7

Using the formula for the area of a triangle

I can use the formula for the area of a triangle to calculate missing side lengths.

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Lesson slides

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Lesson details

Key learning points

0.5 x base x perpendicular height can be used to find the area of any triangle.
Missing sides can be found if the area is known.

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 think the height of the triangle is the slanted height rather than perpendicular.

The base and height to be used must be perpendicular (at a right angle) to each other.

If pupils are not ready to use algebra within this topic, use the correct mathematical terms for the unknown sides alongside the algebra to support their understanding of what the letter represents.

Teacher tip

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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).

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Prior knowledge starter quiz

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6 Questions

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

Correct Answer: height

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

Correct answer: True

False

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

True

Correct answer: False

Q4.
Calculate the area of a triangle with a base of 13 cm and a perpendicular height of 3 cm (you do not need to give the units).

Correct Answer: 19.5 cm$$^2$$, 19.5

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

Correct Answer: identical, congruent

Q6.
Which of these is the correct way to calculate the area of this triangle?

base $$\times$$ perpendicular height $$\times$$ 0.2

base $$\times$$ perpendicular height $$\div {1 \over 2}$$

Correct answer: $$b \times h \times {1 \over 2}$$

$$bh \times 2$$

Assessment exit quiz

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6 Questions

Q1.
The base and height of this triangle measure:

13.3 mm and 15.3 mm

Correct answer: 18.3 mm and 15.3 mm

13.3 mm and 18.3 mm

13.3 mm and 19.3 mm

Q2.
Select the correct expression for the area of the triangle.

Correct answer: $$ac \over 2$$

$$ab \over 2$$

$$bc \over 2$$

Q3.
Select the correct expression for the area of the triangle.

$$28bd \over 2$$

$$20bd^{2}t \over 2$$

Correct answer: $$35dt \over 2$$

Q4.
Calculate the missing side length.

Correct Answer: 10 cm, 10

Q5.
Calculate the missing side length.

Correct Answer: 3.3 cm, 3.3

Q6.
Calculate the missing side length.

Correct Answer: 2.5 cm, 2.5

Lesson appears in

UnitMaths / Perimeter and area

Maths

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Using the formula for the area of a triangle

Using the formula for the area of a triangle

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Equipment

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

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

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

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

Q4.Calculate the area of a triangle with a base of 13 cm and a perpendicular height of 3 cm (you do not need to give the units).

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

Q6.Which of these is the correct way to calculate the area of this triangle?

Assessment exit quiz

6 Questions

Q1.The base and height of this triangle measure:

Q2.Select the correct expression for the area of the triangle.

Q3.Select the correct expression for the area of the triangle.

Q4.Calculate the missing side length.

Q5.Calculate the missing side length.

Q6.Calculate the missing side length.

Lesson appears in

UnitMaths / Perimeter and area

Maths

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

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

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

Q4.
Calculate the area of a triangle with a base of 13 cm and a perpendicular height of 3 cm (you do not need to give the units).

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

Q6.
Which of these is the correct way to calculate the area of this triangle?

Q1.
The base and height of this triangle measure:

Q2.
Select the correct expression for the area of the triangle.

Q3.
Select the correct expression for the area of the triangle.

Q4.
Calculate the missing side length.

Q5.
Calculate the missing side length.

Q6.
Calculate the missing side length.