Question

Find the area. Give your answer as a simplified radical.

Answer 1

First we need to know the measure of the side, we can use the next trigonometric function

AE=2

$\tan (30)=\frac{AE}{BE}=\frac{2}{BE}$

we isolate the BE

$BE=\frac{2}{\tan(30)}=2\sqrt[]{3}$

the area of triangle ABE

$A_{\text{ABE}}=\frac{1}{2}\cdot2\cdot2\sqrt[]{3}=\text{ }2\sqrt[]{3}$

For the total area of the rhombus is

$A=4(2\sqrt[]{3})$$A=8\sqrt[]{3}$