+0

# help

0
112
1

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

Jun 17, 2020

#1
+8352
+1

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