the area of the regular octagon is 10.15 cm². what is the measure of the apothem, rounded to the nearest…

Explanation:

Step1: Recall area formula for regular polygon

The area formula for 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 octagon with side - length $s = 1.45$ cm, the perimeter $P=8s$. $P = 8\times1.45=11.6$ cm.

Step2: Solve for the apothem

We know that $A = 10.15$ cm² and $P = 11.6$ cm. Substitute these values into the area formula $A=\frac{1}{2}aP$ and solve for $a$. $10.15=\frac{1}{2}\times a\times11.6$. First, multiply both sides of the equation by 2 to get $2\times10.15=a\times11.6$. $20.3 = 11.6a$. Then, divide both sides by 11.6: $a=\frac{20.3}{11.6}=1.75$ cm.

Answer:

1.75 cm