Starter quiz
Which of the dotted lines shows the perpendicular height of the triangle from the labelled base?- Line a ✓
- Line b
- Line c
- Line d
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- Complete the formula for the area of a triangle. Area = base × perpendicular height ÷ ______
- '2' ✓
Calculate the area of the triangle. ______ cm².- '35' ✓
Calculate the area of the triangle. ______ cm².- '52' ✓
- Calculate the area of a triangle with a base of 15 cm and a perpendicular height of 8 cm. ______ cm².
- '60' ✓
- If a parallelogram has an area of 56 cm² and a base of 8 cm, what is the missing perpendicular height? ______ cm.
- '7' ✓
Exit quiz
- 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.
- '2' ✓
- 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 ÷ ______
- 'base' ✓
Look at the triangle. The missing perpendicular height is ______ cm- '10' ✓
Look at the triangle. The missing perpendicular height is ______ cm.- '6' ✓
Look at the triangle. The missing base length is ______ cm.- '10' ✓
- 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
- Base = 12 cm, Perpendicular height = 7 cm ✓
- Base = 4 cm, Perpendicular height = 21 cm ✓
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Worksheet
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Presentation
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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
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.
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