Question

An isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14. The area of the trapezoid is what?

Answer 1

33 unit^2.

Explanation:

Area of a trapezoid = h(a + b)/ 2 where h = its height and a and b are the lengths of its parallel sides.

If we draw a line perpendicular to the longest base from the endpoint of the smallest base we get a right triangle with 2 angles of 45 degree , and because it is an isosceles trapezoid the base of the triangle = (14 - 8)/2 = 3 units. Since it is a 45-45-90 triangle the height is also 3 units.

So the area = 3 (14 + 8) / 2 = 33 unit^2.