We will first need to find the perimeter and the apothem of the polygon. Then we will use the formula A= 12ap to find the area.
Finding the Perimeter
Since we have a regular octagon whose side length is 12.4inches, we can find the perimeter by multiplying 8 by 12.4.
8* 12.4= 99.2inches
The perimeter of the given polygon is 99.2inches.
Finding the Apothem
Let's draw the apothem on our diagram.
Notice that the given length 30inches is twice the length of the apothem. Therefore, we can write an equation for a and find its value.
30 = 2a ⇔ a= 15
Finding the Area
To find the area of the given regular polygon, we will substitute a=15 and p= 99.2 in the formula A= 12ap.
