Volume of a prism is depth times area of a face.
We know the hexagon is regular, so we can split it into six equal triangles.
[tex] \frac{1}{6} ^ {th} [/tex] of 360 is 60°, so the top angle is 60°. The two other angles must be equal, 180-60=120, 120÷2=60. So we know it is an equalateral triangle, so the two other lengths are also 12ft. If we split one of those triangles in half, we can find the height of the triangle. Half the bottom is 6ft, the hypotenuse is 12ft and the height is a. a²+b²=c² a²+6²=12² a²+36=144 a²=108 a=√108
Back to the larger triangles. The area of a triangle is [tex] \frac{1}{2}bh[/tex]. [tex] \frac{1}{2}[/tex]×12×√108 6×√108 is the area of one triangle, which is a sixth of the hexagon.
6×6×√108 36×√108
36×√108 is the area of the hexagon
Finally multiply it by 15 15×36×√108=540×√108
