Question

Which one is the apothem of an octagon if its perimeter is 16 cm?

A) 2 cm
B) 4 cm
C) 6 cm
D) 8 cm

Answer 1

The apothem of the octagon with a perimeter of 16 cm is 2 cm, so the correct option is (A) 2 cm.

Step-by-step explanation:

For a regular octagon, the formula for the perimeter (P) is given by P = 8 times the side length.

In this case, the perimeter is 16 cm, so the side length is 16/8 = 2 cm.

The apothem (a) of a regular octagon can be found using the formula a = (s/2) times (1 + sqrt(2)), where s is the side length.

Substitute the side length into the formula: a = (2/2) times (1 + sqrt(2)) = 1 + sqrt(2) cm.

Confirm that the correct option is (A) 2 cm, as 1 + sqrt(2) is approximately 2 cm.