Question

Each side of the regular hexagon below measures 8 cm. What is the area of the hexagon?

Answer 1

Answer

Find out the area of the regular hexagon.

To prove

As given in the question

Hexagon is regular thus it is made up of the six equilateral triangle.

Thus area  of the regular hexagon is 6 times the area of a equilateral triangle.

Each side of the regular hexagon  measures 8 cm.

Formula

$Area\ of\ hexagon = 6\times \frac{\sqrt{3}a^{2}}{4}$

where a represented the side.

$Area\ of\ hexagon = 6\times \frac{\sqrt{3}\times 8\times 8}{4}$

$Area\ of\ hexagon = 6\times \sqrt{3}\times 8\times 2$

$Area\ of\ hexagon = 96 \sqrt{3}\ unit^{2}$  

Therefore the option (a) is correct .

Answer 2

A regular hexagon can be split into 6 congruent equilateral triangles.
the area of an equilateral triangle is √3*s²/4, where s is the side length
Area of the hexagon
= 6*√3*8²/4
= 96√3 square centimeters