Question

Which regular polygon with an apothem of 5 inches, will have a perimeter that is the closest to the circumference of a circle with a diameter of 10.8 inches?

square
pentagon
hexagon
octagon

Answer 1

The regular polygon with an apothegm of 5 inches, that has a perimeter that is closest to the circumference of a circle with a diameter of 10.8 inches is an octagon. The correct answer is D.

I honestly don't take credit for this answer, lol.
I looked it up, and that was the answer given by Oopsydaisy, also on this site.

Answer 2

Hexagon

Explanation:

Let us find the circumference of the circle first. We are given its diameter as 10.8 inches. The formula to find the perimeter of the circle is

`P=2\pi*r`

r is radius which is half of diameter that is 10.8÷2 = 5.4

hence ,
`P=2*\pi*5.4`

`\pi=3.14`

P=2*3.14*5.4=33.912 inches

Now let us see the perimeter of each of them with 5 inches as side

Square : 4*5=20 inches

Pentagon : 5*5 = 25 inches

Hexagon : 6*5=30 inches

Octagon : 8*5=40 inches

Hence It is close to perimeter of Hexagon