SOLUTION: I was wondering if you could help me with a problem. I have a problem that is asking me to find the volume of a pentagonal pyramid with base or side measure of 23,and height of 27

Question 891237: I was wondering if you could help me with a problem. I have a problem that is asking me to find the volume of a pentagonal pyramid with base or side measure of 23,and height of 27. Help please?

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The volume is 1/3 times the area of the base, times the height.
You may have been given a formula to calculate the area of a regular polygon.
A regular pentagon (one whose sides all have the same length and whose angles all have the same measure) can be cut, like a pizza into 5 identical isosceles triangles.
In your pentagon, those triangles would have a base length of 23 and angles measuring 72, 54, and 54 degrees.
The height would be , and the tangent of is approximately
.
So the area of the pentagon is approximately
.
Let's round that to 1820.
Then, the volume of a pyramid with a base area of 1820 area units and a height of 27 units , calculated in volume units, would be
.
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