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If the area of the regular hexagon is 90, what is the area of the purple region?

 

 Jun 17, 2020
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The area of a regular hexagon A is related to its length L by 

\(A = \dfrac{3\sqrt 3}2 L^2\)

 

Consider the top white isosceles triangle.

The base is \(2L\sin 60^\circ = \sqrt 3 L\). This is also the length of the rectangle.

 

The width of the rectangle is \(L\), so the area of the rectangle is \(\sqrt 3 L^2 = \dfrac23 A\).

 

The area of rectangle is two thirds of the area of the hexagon, which is 60.

 Jun 17, 2020

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