Question

the area of the regular octagon is 10.15 cm². what is the measure of the apothem, rounded to the nearest hundredth of a centimeter? 1.27 cm 1.75 cm 2.33 cm 2.54 cm 1.45 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.

Step2: Calculate the perimeter of the octagon

For a regular octagon with side length \(s = 1.45\) cm, the perimeter \(P=8s\). So \(P = 8\times1.45=11.6\) cm.

Step3: Solve for the apothem \(a\)

We know \(A = 10.15\) \(cm^{2}\) and \(P=11.6\) cm. From \(A=\frac{1}{2}aP\), we can solve for \(a\). Rearranging the formula gives \(a=\frac{2A}{P}\).
Substitute \(A = 10.15\) and \(P = 11.6\) into the formula: \(a=\frac{2\times10.15}{11.6}\).

$$a=\frac{20.3}{11.6}=1.75$$

Answer:

1.75 cm