Question

If the apothem is 13 square root 3 ft what is the area of the hexagon

Answer 1

The area of the hexagon is
`1,014√(3)\ ft^(2)`

Explanation:

we know that

The area of a regular hexagon is equal to

`A=(1)/(2)Pa`

where

P is the perimeter

a is the apothem

Find the length side of the hexagon

Let

b-----> the length side of the hexagon

Remember that

The formula to calculate the length side given the apothem is equal to

`b=(2a)/(√(3))`

we have

`a=13√(3)\ ft`

substitute

`b=(2(13√(3)))/(√(3))`

`b=26\ ft`

Find the perimeter P

`P=6b=6(26)=156\ ft`

Find the area of the hexagon

`A=(1)/(2)(156)(13√(3))=1,014√(3)\ ft^(2)`