Question

here's the question

Dear Dr. Math,

I wanted tto find the area of this hexagon. I few the apothem as I've shown. Then I measured the apothem and perimeter. I used the formula a=1/2ap and got 3.2cm^2 for the area but that seems way too small for me. I think my teacher got lucky when she used that formula because it only works in a while. Do you agree?

K. L. Ooless

I need help with this and i need to know how to show the work.

Answer 1

The area of a hexagon is 1/2 a*P

Answer 2

The formula works all the time for a <b>regular </b>polygon.

However, the way you wrote the formula makes no sense. You cannot use the same variable "a" for area and for apothem.
Furthermore, we cannot draw diagrams in this forum, and lastly you did not give the dimensions of your hexagon, so I cannot check your answer.

Here is why the formula works.
A hexagon has 6 equal triangles, so lets find the area of one of them and multiply by 6
Let the base of the triangle be n, and its height h
so each triangle is (1/2)nh
But isn't the height h of the triangle the same as the apothem a ?
so each triangle is (1/2)an
so lets multiply by 6 to get the total area
which is (1/2)a(6n)
BUT, isn't 6n the perimeter ????

So the area is (1/2)a(perimeter)

Answer 3

60