Question

Find the area of a regular octagon with an apothem length of 10 and a side length of 6.

Answer 1

A = 240 units²

Explanation:

the area (A) of a regular polygon is

A =
`(1)/(2)` pa ( p is the perimeter and a the apothem )

here p = 8 × 6 = 48 ( an octagon has 8 sides ) and a = 10 , then

A =
`(1)/(2)` × 48 × 10 = 24 × 10 = 240 units²

Answer 2

Explanation:

Preliminary task

Draw a regular octagon.

Draw a perpendicular from the side's midpoint to the center. (That is the apothem).

Draw two radii from the center of the side to the center of of the octagon. The endpoints of these two radii is the endpoints of the octagon's side.

The octagon has 8 such triangles.

Area one triangle

Area = 1/2 * side * apothem

side = 6

apothem = 10

Area = 1/2 6 * 10

Area = 30

Area of 8 such triangles.

Area = 8 * area of 1 triangle

area 1 triangle = 30

Area of 8 such triangles = 30*8 = 240

Answer 240