Question

find the area of each of the following regular polygons.
a.
b.
a. the area of the regular hexagon is
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall the formula for the area of a regular polygon

The formula for the area of a regular polygon is \(A=\frac{1}{2}Pa\), where \(P\) is the perimeter and \(a\) is the apothem.

Step2: Calculate the perimeter of the hexagon

For a regular hexagon with side length \(s = 6\space cm\), the perimeter \(P=6s\). So \(P = 6\times6=36\space cm\).

Step3: Identify the apothem

The apothem \(a = 3\sqrt{3}\space cm\).

Step4: Substitute into the area formula

Substitute \(P = 36\) and \(a=3\sqrt{3}\) into \(A=\frac{1}{2}Pa\).

$$
LATEXBLOCK0
$$

Answer:

\(54\sqrt{3}\space cm^{2}\)