SOLUTION: A pyramid's base is hexagonal. The length of each hexagon side is 12 cm. The length of each pyramid's sloping edge is 24 cm. How to calculate the pyramid's surface area and volume?

Question 1082413: A pyramid's base is hexagonal. The length of each hexagon side is 12 cm. The length of each pyramid's sloping edge is 24 cm. How to calculate the pyramid's surface area and volume?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You are given the measure of a side of the base, b, and the slant height, s. In order to calculate the volume, you need the apothem, a, of the base which is the measure of the distance from the center of the base to the midpoint of one side. For a regular hexagon, the apothem is the height of an equilateral triangle with sides congruent to a side of the hexagon. I leave the calculation of this value as an exercise for the student. And then you need the height, h, which is the measure from the center of the base to the apex. Use Pythagoras:

Then the volume of your pyramid is:

For the surface area, you need to decide whether you want the Lateral Surface Area (just the sides excluding the area of the base) or the Total Surface Area (sides AND the base):

John

My calculator said it, I believe it, that settles it

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