Answer
750 $cm^{2}$
Work Step by Step
Given in a regular octagon the approximate ratio of the length of an apothem to the length of a side is 6:5
The length of apothem of regular octagon a = 15 cm
The area of a regular polygon whose apothem has length a and whose perimeter P is given by A = $\frac{1}{2}$ ap
Lets take the ratio of apothem and side ratio 6:5. By proportionality constant x
The apothem a = 6x
side s= 5x
But given apothem a = 15cm
a = 6x = 15
x = $\frac{15}{6}$ = 2.5 cm
Side of octagon s = 5x = 5* 2.5 = 12.5cm
The perimeter of octagon P = 8s = 8 * 12.5 = 100 cm
The area of octagon A = $\frac{1}{2}$ ap
= $\frac{1}{2}$ *15 * 100 = 750 $cm^{2}$
