Question

find the area of a regular hexagon with an apothem of 3.5 cm and a side length of 4 cm.

Explanation:

Step1: Find the perimeter

A regular hexagon has 6 equal - length sides. Given side length \(s = 4\) cm, the perimeter \(P\) is the product of the number of sides and the side - length.
\(P=6\times s=6\times4 = 24\) cm

Step2: Use the area formula

The area formula for a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter. Given \(a = 3.5\) cm and \(P = 24\) cm.
\(A=\frac{1}{2}\times3.5\times24\)
\(A = 42\) \(cm^{2}\)

Answer:

\(42\)