Question

the pentagon below has an area of 8.3 square centimeters. what is the approximate length of the apothem? 0.4 cm 0.8 cm 1.5 cm 1.9 cm 2.2 cm

Explanation:

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

The formula for the area of a regular polygon is \(A=\frac{1}{2}aP\), where \(A\) is the area, \(a\) is the apothem, and \(P\) is the perimeter.
For a regular pentagon with side length \(s = 2.2\) cm, the perimeter \(P=5s\). So \(P = 5\times2.2=11\) cm.

Step2: Solve for the apothem \(a\)

We know \(A = 8.3\) square centimeters and \(P=11\) cm. From \(A=\frac{1}{2}aP\), we can solve for \(a\).
Rearrange the formula to \(a=\frac{2A}{P}\).
Substitute \(A = 8.3\) and \(P = 11\) into the formula: \(a=\frac{2\times8.3}{11}=\frac{16.6}{11}\approx1.5\) cm.

Answer:

\(1.5\) cm (the third option)