GwenevereN749485 GwenevereN749485
  • 04-11-2022
  • Mathematics
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Find the area. Give your answer as a simplified radical.

Find the area Give your answer as a simplified radical class=

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CrissV753934 CrissV753934
  • 04-11-2022

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

AE=2

[tex]\tan (30)=\frac{AE}{BE}=\frac{2}{BE}[/tex]

we isolate the BE

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

the area of triangle ABE

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

For the total area of the rhombus is

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

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