Question

The lengths of the parallel sides of an isosceles trapezoid are 8 in. and 16 in., respectively. If the diagonal bisects the base angle, what is the area of the trapezoid?

Answer 1

\[\tan(2A)=\frac{ \sqrt{x ^{2}-4^{2}} }{ x }\] \[\tan(A)=\frac{ \sqrt{x ^{2}-4^{2}} }{ 20 }\] Knowing that: \[\tan(2A)=\frac{ 2\tan(A) }{ 1-\tan ^{2}(A) }\] Try solving for x.