Given:
A figure of a triangular prism.
Height of triangular base = [tex]9\dfrac{2}{3}[/tex] yd
Base of triangular base = 4 yd
Height of prism = 4 yd.
To find:
The volume of the triangular prism.
Solution:
Volume of a triangular prism is:
[tex]V=Bh[/tex] ...(i)
Where, B is the area of triangular base and h is the height of the prism.
Area of triangular base is:
[tex]B=\dfrac{1}{2}\times base\times height[/tex]
[tex]B=\dfrac{1}{2}\times 4\times 9\dfrac{2}{3}[/tex]
[tex]B=2\times \dfrac{29}{3}[/tex]
[tex]B=\dfrac{58}{3}[/tex]
Putting [tex]B=\dfrac{58}{3}[/tex] and h=4 in (i), we get
[tex]V=\dfrac{58}{3}\times 4[/tex]
[tex]V=\dfrac{232}{3}[/tex]
[tex]V=77.33...[/tex]
[tex]V\approx 77.3[/tex]
The volume of the triangular prism is 77.3 cubic yards. Therefore, the correct option is 2.
