Question 891237
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 {{{23*tan(54)}}} , and the tangent of {{{54^o}}} is approximately
{{{tan(54^o)=1.3764}}} .
So the area of the pentagon is approximately
{{{23*23*1.3764*5/2=1820.289}}} .
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
{{{(1/3)*1820*27=16380}}} .