The area of a triangle — Mathematics, 11–13 years
How to measure the amount of flat space inside a triangle. Mathematics, 11–13 years.
Half of a matching rectangle
The area of a triangle is half the area of a rectangle with the same base and the same perpendicular height. That is why the rule is base × height ÷ 2. The height must meet the base at a right angle; it is not simply any sloping side.
Why divide by two?
A triangle can be paired with an identical copy to make a rectangle or parallelogram. The two triangles share the total space equally, so one triangle takes half of it. This solves the problem of measuring a pointed shape without counting every tiny square inside it.
An area of 20 square centimetres
A triangle has a base of 8 cm and a perpendicular height of 5 cm. Multiply: 8 × 5 = 40 square centimetres, which is the matching rectangle. Divide by 2: 40 ÷ 2 = 20. So the triangle covers 20 cm², not 20 cm, because area measures space.
Using the sloping side
Many people use the longest sloping side as the height because it is easy to notice and measure. That is a sensible first guess, but height means the shortest straight distance to the chosen base, meeting it at 90°. A sloping side works only when it is perpendicular to the base.
Covering triangular spaces
The rule helps estimate the amount of paint for a triangular wall, fabric for a pennant or soil for a triangular garden bed. You still need sensible measurements and the same units. It gives the covered surface, not the length of the border around it.
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