Given that is a square of side length cm, find the area of , and approximate the result to the nearest integer.
Draw to form , and find the area of the right-angled triangle.
If two triangles share the same base and their vertices lie on a straight line parallel to the base, then the triangles are equal in area.
and share a common base and their vertices lie on a line parallel to that base (because opposite sides of a square are parallel). Therefore,
Triangles with congruent bases on one straight line that have a common vertex are equal in area. Therefore, the area of is equal to that of , and the area of is equal to half the area of .