the area of the regular octagon is approximately 54 cm². what is the length of line segment ab, rounded to…

Answer:

3.4 cm

Explanation:

Step1: Recall area - apothem formula

$A = \frac{1}{2}aP$, where $A$ is area, $a$ is apothem, $P$ is perimeter. Given $A = 54$ cm² and apothem $a = 4$ cm.

Step2: Find the perimeter $P$

$54=\frac{1}{2}\times4\times P$. Solving for $P$, we get $P=\frac{54\times2}{4}=27$ cm.

Step3: Find side - length

A regular octagon has 8 equal sides. Let side - length be $s$. Then $P = 8s$. Since $P = 27$ cm, $s=\frac{27}{8}=3.375\approx3.4$ cm. Segment $AB$ is a side of the octagon, so length of $AB$ is approximately 3.4 cm.