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# help!

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A rhombus has a perimeter of 8 and an angle of 60 degrees.  What is its area?

May 7, 2020

#1
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if one of the angles is $$60^\circ$$, then we know the rhombus is made up of four 30-60-90 right triangles, with the hypotenuses making up the perimeter. we know that the hypotenuse is $$8\div4=2$$, so one leg has a length of $$1$$ and the other leg is the length $$\sqrt3$$. this means that the lengths of the diagonals are $$2$$ and $$2\sqrt3$$, so the area of the rhombus is $$2 \times 2\sqrt3 = \boxed{4\sqrt3}$$.

May 7, 2020
#2
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I got the same answer nice!

LuckyDucky  May 7, 2020