Quest of Nine

The Book

Area of a triangle

Look at these right-angled triangles.

right-angled triangle right-angled triangle right-angled triangle right-angled triangle

Move your mouse pointer over the triangles. You will see that each one is half a rectangle.

So the area of each triangle is half of its rectangle's area

12cm x 20cm right-angled triangle This triangle is half of a rectangle which is 20cm wide and 12cm high.
area = 20cm x 12cm = 240cm2

So, the area of the triangle = 240 ÷ 2 = 120cm2


Non right-angle triangles

Look at this non right-angle triangle (This one is called a Scalene because its sides are all different lengths.)

Scalene triangle The triangle is half a parallelogram. So this triangle's area is half of the parallelogram's.
Since a parallelogram's area is its length times its height, then for a scalene

area = width x height ÷ 2


Look at these scalenes.

Roll your mouse over a scalene to see its parallelogram.

scalene scalene scalene scalene


Area = square
Check ittick

Not to scale

12cm x 20cm