Question

Find the area of a regular hexagon if the apothem is 8sqrt3 m, and a side is 16m. Round to the nearest whole number.

Answer options: 998, 665, 222, 1330

Answer 1

Option 2. 665 m² is the correct answer.

Explanation:

It has been given in the hexagon apothem is 8√3 and one side of the hexagon is 16 m.

We have to calculate the area of regular hexagon.

Area of hexagon = 6 × area of a triangle formed with one side of hexagon.

= 6 × 1/2( Base × height)

= 3 × (8√3 × 16)

= 384√3 = 665 m²

So the answer is 665 m².

Answer 2

Answer: SECOND OPTION.

Explanation:

To calculate the area of the regular hexagon you must apply the following formula:

`A=(P*a)/(2)`

Where P is the perimeter and a is the apothem.

The perimeter is:

`P=6*s`

Where s is the lenght of a side.

Then:

`P=6*16m=96m`

Then, the area is:

`A=(96m*8√(3)m)/(2)\\A=665m^(2)`