Question

W

h
Triangular Prismn width
17 inches, length = 12 inches and height = 21 inches.
V=
inches

Answer 1

V = 0.5wlh = 0.5(17)(12)(21) = 2142in³.

Answer 2

`\boxed {\boxed {\sf v=2142 \ in^3}}`

Explanation:

The volume of a triangular prism can be found by multiplying the area of the base by the height.

`v=B*h`

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.

`B= (1)/(2) *w*l`

Substitute this formula in for B.

`v= ((1)/(2) *w*l)*h`

We know that the width is 17 inches, the length is 12 inches, and the height is 21 inches. Substitute the values in.

`w= 17 \ in \\l= 12 \ in \\h= 21 \ in`

`v= ((1)/(2)* 17 \ in * 12 \ in ) * 21 \ in`

Solve inside the parentheses first. Multiply 17 and 12.

`v=((1)/(2)*204 \ in^2) * 21 \ in`

Finish solving the parentheses by multiplying by 1/2 or dividing by 2.

`v=102 \ in ^2 * 21 \ in`

Multiply.

`v=2142 \ in^3`

The volume of the triangular prism is 2,142 cubic inches.