Given:
The sides of an equilateral triangle base are 10 yds. The height of the prism is 29 yds.
To find:
The volume of the prism.
Solution:
The formula of the volume of the triangular prism is given by:
[tex]V=\text{ (area of base)}\times\text{ (height of the prism)}[/tex]
It is known that the area of the equilateral triangle is given by:
[tex]A=\frac{\sqrt[]{3}}{4}(side)^2[/tex]
So, the area of the base of the triangular prism is:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}(10)^2 \\ =\frac{1.732}{4}\times100 \\ =\frac{173.2}{4} \\ =43.30 \end{gathered}[/tex]
Now, the volume of the given triangular prism is:
[tex]\begin{gathered} V=43.30\times29 \\ =1255.7\text{ yad\textasciicircum{}3} \end{gathered}[/tex]
