MathNet 2020 — Math Olympiad Vault — Part 05 Question 88

In convex pentagon $A B C D E$, $A B = B C$, $C D = D E$, $\angle A B C = 100^{\circ}$, $\angle C D E = 80^{\circ}$, and $B D^{2} = \frac{100}{\sin 100^{\circ}}$. Find the area of the pentagon.