Find the area of a regular hexagon?

Question

with apothem of 6m long.

I think the formula for area is A= 1/2 Perimeter times apothem

A= 1/2 ( perimeter times 6)

Answer 1

You have the A=1/2 (Perimeter x 6) thing right.
Just for reference:
To calculate the apothem you have to divide the Hexagon into six parts, now depending on your information, figure out which method to figure out the apothem(I use simple trigonometry (sine, cosine, tangent), or depending on the case a 30 60 90 triangle), Once you have the apothem calculate the perimeter (add all sides). Now multiply the perimeter by the apothem, and there is your answer.

Answer 2

The apothem is the line from the center that goes to the midpoint of one of the sides. So, A=.5(perimx6)

Use trigonometry to find the perimeter. The apothem always makes a right angle with the side it is touching. So a triangle consisting of the apothem, half of a side, and the line segment from the center to an adjacent vertex would be a right triangle, to which trigonometry can be applied. You know the measure of the angle closest to the center by dividing 360 degrees by the number of sides the polygon has and then dividing it again by 2. This way you can find the remaining non-right angle and use these with sin, cos, and tan to find the length of the side of the triangle adjacent to the apothem and on the right angle. This is half of a side of the hexagon. Times it by 12 to get your perimeter.

Answer 3

A regular hexagon is like 6 equal triangles. So divide the hexagon into 6 equal triangles, calculate the area of a single of those triangles, multiply by 6 and you have your answer. I think this should work.

Answer 4

Do your own homework. You're cheating yourself by asking other people to do your homework for you. If you need help, ask someone HOW to do the problem.