Question

find the volume of the triangular prism. use the formula: v = bh b = area of the triangle base 3 in v = ? in³ 9 in 4 in use a

Explanation:

Step1: Calculate the area of the triangular base (B)

The formula for the area of a triangle is \( B=\frac{1}{2}\times base\times height \). Here, the base of the triangle is \( 4 \) in and the height is \( 3 \) in. So, \( B = \frac{1}{2}\times4\times3 \).
\( \frac{1}{2}\times4\times3 = 2\times3 = 6 \) square inches.

Step2: Calculate the volume of the triangular prism (V)

The formula for the volume of a triangular prism is \( V = Bh \), where \( h \) is the length of the prism (the distance between the two triangular bases). Here, \( B = 6 \) square inches and \( h = 9 \) in. So, \( V = 6\times9 \).
\( 6\times9 = 54 \) cubic inches.

Answer:

\( 54 \)