Question

Find the area of a regular pentagon with an apothem of 11 units. *

364 square units
O 440 square units
516 square units
O 166 square units

Answer 1

440 square units

Explanation:

We can find half of a side of the pentagon with the expression

`tan(36\°)=(s_(half) )/(11)`

Because, as a regular polygon, all its sectors have the same central angle, and the apothem divides equally each sector in two equal parts.

`s_(half) \approx 8`

Therefore, half of a side is 8 units long, which means each side measures 16 units.

Now, the area of a penthagon is defined by

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

Where
`p` is the perimeter and
`a` is the apothem. Where the perimeter is the sum of all sides, which is 80 units.

`A= (80 * 11)/(2) =440 \ u^(2)`

Therefore, the right answer is the second choice.