Answer:
[tex]\boxed {\boxed {\sf v=2142 \ in^3}}[/tex]
Step-by-step explanation:
The volume of a triangular prism can be found by multiplying the area of the base by the height.
[tex]v=B*h[/tex]
The area of a triangle can be found by multiplying the base, height, and 1/2. In this problem, the base and height are width and length.
[tex]B= \frac{1}{2} *w*l[/tex]
Substitute this formula in for B.
[tex]v= (\frac{1}{2} *w*l)*h[/tex]
We know that the width is 17 inches, the length is 12 inches, and the height is 21 inches. Substitute the values in.
[tex]w= 17 \ in \\l= 12 \ in \\h= 21 \ in[/tex]
[tex]v= (\frac{1}{2}* 17 \ in * 12 \ in ) * 21 \ in[/tex]
Solve inside the parentheses first. Multiply 17 and 12.
[tex]v=(\frac{1}{2}*204 \ in^2) * 21 \ in[/tex]
Finish solving the parentheses by multiplying by 1/2 or dividing by 2.
[tex]v=102 \ in ^2 * 21 \ in[/tex]
Multiply.
[tex]v=2142 \ in^3[/tex]
The volume of the triangular prism is 2,142 cubic inches.
