Question

What is the area of an isosceles trapezoid if the length of its shorter base is 18 cm, the length of an altitude is 9 cm, and the measure of the acute angle is 45º.

Answer 1

Check the picture below.

since we know the acute angle is 45°, that angle with the bottom base and the slanted line and the altitude make a 45-45-90 triangle, and thus we can get the value of that section at the bottom, as you see in the picture, thus the longer base is 9 + 18 + 9, or 36.

$\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{bases}{parallel~sides}\\ h=height\\ ---------\\ a=18\\ b=36\\ h=9 \end{cases}\implies A=\cfrac{9(18+36)}{2} \\\\\\ A=\cfrac{9(54)}{2}\implies A=243$