Question

Find the area of the regular octagon if the apothem is 3 cm and a side is 2.5 cm? Round to the nearest whole number.

i really dont understand the whole thing.

Answer 1

Should be `"30 cm"^2`.

Explanation:

The apothem is a line segment from the center to the midpoint of one of its sides. You can first divide the octagon into `8` small triangles. Each triangle has an area of

`"2.5 cm"/2 xx "3 cm" = "3.75 cm"^2`

Then

`"3.75 cm"^2 xx 8 = "30 cm"^2`

is the total area of the octagon.

Hope you understand. If not, please tell me.

Answer 2

I get `30 \ "cm"^2`.

Explanation:

Given the apothem length, the area of a regular polygon becomes

`A=1/2*p*a`

`p` is the perimeter of the regular polygon

`a` is the apothem of the regular polygon

Here, we get `p=8*2.5=20 \ "cm"`, `a=3 \ "cm"`.

So, plugging in the given values, we get

`A=1/2*20 \ "cm"*3 \ "cm"`

`=10 \ "cm" * 3 \ "cm"`

`=30 \ "cm"^2`

So, the regular octagon will have an area of `30 \ "cm"^2`.