Question

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

Answer 1

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* (√(3)a^(2))/(4)`

where a represented the side.

`Area\ of\ hexagon = 6* (√(3)* 8* 8)/(4)`

`Area\ of\ hexagon = 6* √(3)* 8* 2`

`Area\ of\ hexagon = 96 √(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