Question

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

Explanation:

Step1: Calculate the perimeter

A regular hexagon has 6 sides. Given side length \(s = 4\) cm.
Perimeter \(P=6s\)
\(P = 6\times4=24\) cm

Step2: Use the formula for the area of a regular polygon

The formula for the area \(A\) of 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.
\(A=\frac{1}{2}\times3.5\times24\)
First, calculate \(\frac{1}{2}\times24 = 12\)
Then, \(A=12\times3.5\)
\(A = 42\)

Answer:

\(42\)