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Year 6

Use the area of a triangle to calculate unknown measurements

I can calculate unknown dimensions of a triangle with a specified area.

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Share activities with pupils
New
New
Year 6

Use the area of a triangle to calculate unknown measurements

I can calculate unknown dimensions of a triangle with a specified area.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. The area of a triangle is half the area of a parallelogram with the same perpendicular base and height.
  2. The area of a triangle can be calculated using the formula area = base × perpendicular height ÷ 2
  3. A missing perpendicular height in a triangle can be found using the formula area × 2 ÷ base
  4. A missing base in a triangle can be found using the formula area × 2 ÷ perpendicular height

Common misconception

When drawing triangles with a given area pupils may create a factor pair of the triangle's area when drawing the base and perpendicular height. The factor pair refers to the surrounding parallelogram.

For pupils who are making this mistake, encourage them to sketch the parallelogram around the triangle, reminding them to double the triangle area before finding the factor pairs.

Keywords

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

  • Perpendicular - Two lines are perpendicular if they meet at a right angle.

The learning in this lesson can be made more powerful by having physical triangles rather than the ones on the screen. This will allow you to demonstrate that a triangle is half of a parallelogram and that the base can be in various orientations, not just horizontal.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Which of the dotted lines shows the perpendicular height of the triangle from the labelled base?
An image in a quiz
Correct answer: Line a
Line b
Line c
Line d
Q2.
Complete the formula for the area of a triangle. Area = base × perpendicular height ÷
Correct Answer: 2
Q3.
Calculate the area of the triangle. cm².
An image in a quiz
Correct Answer: 35
Q4.
Calculate the area of the triangle. cm².
An image in a quiz
Correct Answer: 52
Q5.
Calculate the area of a triangle with a base of 15 cm and a perpendicular height of 8 cm. cm².
Correct Answer: 60
Q6.
If a parallelogram has an area of 56 cm² and a base of 8 cm, what is the missing perpendicular height? cm.
Correct Answer: 7

Exit quiz

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6 Questions

Q1.
Complete the formula you could use if the area and perpendicular height of a triangle are known but the base is not: base = area × ÷ perpendicular height.
Correct Answer: 2
Q2.
Complete the formula you could use if the area and base of a triangle are known but the perpendicular height is not: perpendicular height = area × 2 ÷
Correct Answer: base
Q3.
Look at the triangle. The missing perpendicular height is cm
An image in a quiz
Correct Answer: 10
Q4.
Look at the triangle. The missing perpendicular height is cm.
An image in a quiz
Correct Answer: 6
Q5.
Look at the triangle. The missing base length is cm.
An image in a quiz
Correct Answer: 10
Q6.
A triangle has an area of 42 cm². Which of these could be its base and perpendicular height?
Base = 3 cm, Perpendicular height = 7 cm
Base = 6 cm, Perpendicular height = 7 cm
Correct answer: Base = 12 cm, Perpendicular height = 7 cm
Correct answer: Base = 4 cm, Perpendicular height = 21 cm