Question

1. find the area of a regular hexagon whose apothem is 1.7 cm and side length 2 cm. 10.2 cm² 3.4 cm² 20.4 cm² 6.8 cm²

Explanation:

Step1: Find the perimeter

A regular hexagon has 6 sides. Given side length \(s = 2\) cm.
Perimeter \(P=6s\)
\(P = 6\times2=12\) cm.

Step2: Use the area formula for regular polygons

The area formula for a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter.
Given \(a = 1.7\) cm and \(P=12\) cm.
\(A=\frac{1}{2}\times1.7\times12\)
First, calculate \(\frac{1}{2}\times12 = 6\).
Then \(A=6\times1.7\)
\(A = 10.2\) \(cm^{2}\)

Answer:

\(10.2\) \(cm^{2}\)