Question

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

Answer 1

Answer:

The area of the hexagon is $1,014\sqrt{3}\ ft^{2}$

Step-by-step explanation:

we know that

The area of a regular hexagon is equal to

$A=\frac{1}{2}Pa$

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

$b=\frac{2a}{\sqrt{3}}$

we have

$a=13\sqrt{3}\ ft$

substitute

$b=\frac{2(13\sqrt{3})}{\sqrt{3}}$

$b=26\ ft$

Find the perimeter P

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

Find the area of the hexagon

$A=\frac{1}{2}(156)(13\sqrt{3})=1,014\sqrt{3}\ ft^{2}$