Question

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

Answer 1

1350
`√(3)` units²

Explanation:

The regular hexagon consists of 6 equiangular triangles

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

A =
`(s^2√(3) )/(4)` ( s is the side length )

Here s = 30 , then

A =
`(30^2√(3) )/(4)` =
`(900√(3) )/(4)` = 225
`√(3)` units²

Thus the area of the regular hexagon is

area = 6 × 225
`√(3)`

= 1350
`√(3)` units² ← exact value

≈ 2338.3 units² ( to 1 dec. place )