Question

What is the area of the regular pentagon below

Answer 1

Answer:

A

Step-by-step explanation:

By definition, all sides of a regular polygon are equal in length. If you know the length of one of the sides, the area is given by the formula:

$A=\dfrac{s^2\cdot n}{4\tan \frac{180^{\circ}}{n}},$

where s is the side length, n is the number of sides.

In your case, s=20 ft, n=5,so

$A=\dfrac{20^2\cdot 5}{4\tan \frac{180^{\circ}}{5}}=\dfrac{400\cdot 5}{4\tan 36^{\circ}}=\dfrac{500}{0.73}\approx 688.2\ ft^2$

Answer 2

For this case we have that by definition, the polygon area shown is given by:

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

Where:

p: It is the perimeter

a: It is the apothem

So, the perimeter is:

$p = 5 * 20\\p = 100 \ ft$

On the other hand, the apothem is given by:

$tag (36) = \frac {10} {a}\\a = \frac {10} {tag (36)}\\a = \frac {10} {0.72654253}\\a = 13.7638191669247$

Finally, the area is:

$A = \frac {100 * 13.7638191669247} {2}\\A = 688.19096$

Rounding off we have:$688.2 \ ft ^ 2$

Answer:

Option A