Question

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

Answer 1

Answer:

440 square units

Step-by-step explanation:

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

$tan(36\°)=\frac{s_{half} }{11}$

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

$A=\frac{p \times a}{2}$

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

$A= \frac{80 \times 11}{2} =440 \ u^{2}$

Therefore, the right answer is the second choice.