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)=(AE)/(BE)=(2)/(BE)`

we isolate the BE

`BE=(2)/(\tan(30))=2\sqrt[]{3}`

the area of triangle ABE

`A_{\text{ABE}}=(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}`