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.
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.
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Lesson details
Key learning points
- The area of a triangle is half the area of a parallelogram with the same perpendicular base and height.
- The area of a triangle can be calculated using the formula area = base × perpendicular height ÷ 2
- A missing perpendicular height in a triangle can be found using the formula area × 2 ÷ base
- A missing base in a triangle can be found using the formula area × 2 ÷ perpendicular height
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.
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.
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 (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.
Which of the dotted lines shows the perpendicular height of the triangle from the labelled base?
Line b
Line c
Line d
Q2.
Complete the formula for the area of a triangle. Area = base × perpendicular height ÷
Q3.
Calculate the area of the triangle. cm².
Q4.
Calculate the area of the triangle. cm².
Q5.
Calculate the area of a triangle with a base of 15 cm and a perpendicular height of 8 cm. cm².
Q6.
If a parallelogram has an area of 56 cm² and a base of 8 cm, what is the missing perpendicular height? cm.
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.
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 ÷
Q3.
Look at the triangle. The missing perpendicular height is cm
Q4.
Look at the triangle. The missing perpendicular height is cm.
Q5.
Look at the triangle. The missing base length is cm.
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