Question

What is the area of the regular hexagon ABCEF? Explain your reasoning.

Answer 1

Answer:

1350$\sqrt{3}$ units²

Step-by-step explanation:

The regular hexagon consists of 6 equiangular triangles

The area (A) of a equilateral triangle is calculated as

A = $\frac{s^2\sqrt{3} }{4}$ ( s is the side length )

Here s = 30 , then

A = $\frac{30^2\sqrt{3} }{4}$ = $\frac{900\sqrt{3} }{4}$ = 225$\sqrt{3}$ units²

Thus the area of the regular hexagon is

area = 6 × 225$\sqrt{3}$

        = 1350$\sqrt{3}$ units² ← exact value

         ≈ 2338.3 units² ( to 1 dec. place )