Question

What is the perimeter of a regular octagon to the nearest centimeter if the apothem is 6 cms

a) 5
b) 40
c) 20
d) 68​

Answer 1

To find the perimeter of a regular octagon (an eight-sided polygon) when the apothem is given, you can use the following formula:

Perimeter = 8 * Side Length

In a regular octagon, the apothem (the distance from the center to the midpoint of a side) bisects each side into two equal segments, forming 45-45-90 right triangles. So, if the apothem is 6 cm, each side length of the octagon is twice the apothem, which is 2 * 6 cm = 12 cm.

Now, calculate the perimeter:
Perimeter = 8 * Side Length
Perimeter = 8 * 12 cm
Perimeter = 96 cm

Rounding to the nearest centimeter, the perimeter of the regular octagon is approximately 96 cm.

So, none of the provided options (a) 5, (b) 40, (c) 20, or (d) 68 is correct.