Question

Find the area of a regular octagon whose side length is 4.7 in. and the apothem is 6.5 in

Answer 1

122.2 in^2.

Explanation:

WE can divide a regular octagon into 8 triangles with height ( = the apotherm) = 6.5 and base = 4.7.

The area of each triangle is 1/2 * 4.7 *6.5 so #the area of the octagon

= 8 * 1/2 * 4.7 * 6.5

= 122.2 in^2.

Answer 2

For this case we have by definition, that the area of an octagon is given by:

`A = \frac {p * a} {2}`

Where:

p: perimeter

a: apothem

We have that the perimeter is given by the sum of the sides of the octagon:

`p = 8 * 4.7 = 37.6 \ in\\a = 6.5 \ in`

Substituting:

`A = \frac {37.6 * 6.5} {2} = 122.2`

So, the area of the octagon is
`122.2 \ in ^ 2`

Answer:

`122.2 \ in ^ 2`