Question

An isosceles trapezoid has bases of 4 and 10. If the base angle is 45°, find the area.

Answer 1

Imagine breaking up the trapezoid into a rectangle in the middle, and a right-angled triangles on each end.

The trapezoid's longer base therefore has a length of 4 in the rectangle (to match the shorter base), plus 3 in each triangle, to add up to 10 (4 + 3 + 3).

In each triangle, since the width is 3, and the angle is 45 degrees, then the height is also 3.

So the area of the trapezoid is 3 * (10 + 4) / 2 = 3 * 14 / 2 = 42 / 2 = 21