Area
Section: Measurement | Syllabus: Cambridge Primary Mathematics (0845)
Area of Right-Angled Triangles
The area of a rectangle is found by multiplying its length by its width. A right-angled triangle is always exactly half of a rectangle, so its area can be found using the same idea.
- The area of a rectangle = length × width, measured in square units such as cm² or m²
- A right-angled triangle is exactly half of a rectangle - cutting a rectangle along a diagonal from one corner makes two identical right-angled triangles
- So the area of a right-angled triangle = 1/2 × base × height, where the base and height are the two sides that meet at the right angle
- Before calculating exactly, you can estimate by rounding the base and height to easier numbers, then halving their product
The area of the shaded right-angled triangle is exactly half of the whole rectangle's area
Worked Example: Estimating and Calculating the Area of a Right-Angled Triangle
- Question: A right-angled triangle has a base of 11 cm and a height of 6 cm. Estimate the area, then calculate the exact area.
- Step 1: Estimate first: round 11 to 10, so 10 × 6 ÷ 2 = 30
- Step 2: Find the exact rectangle area: 11 × 6 = 66
- Step 3: Halve it, since the triangle is only half of the rectangle: 66 ÷ 2 = 33
- Answer: 33 cm² (close to the estimate of 30, so it is sensible)
Common Mistakes
MistakeForgetting to halve the rectangle's area, using base × height as the triangle's area instead
Fixa right-angled triangle is only half of the rectangle formed from its base and height - always divide by 2
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