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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

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