Question

6 find the volume.
(figure with dimensions 12 in, 9 in, 15 in, 16 in)
9 find the volume.

Explanation:

Step1: Identify the shape (triangular prism)

The figure is a triangular prism. The formula for the volume of a triangular prism is \( V = B \times h \), where \( B \) is the area of the triangular base and \( h \) is the length of the prism.

Step2: Calculate the area of the triangular base

The base of the triangle has a length of \( 9 \) in and a height of \( 12 \) in. The area of a triangle is \( B=\frac{1}{2}\times base\times height \). So, \( B = \frac{1}{2} \times 9 \times 12 \).

$$ B=\frac{1}{2}\times9\times12 = 54 \text{ square inches} $$

Step3: Determine the length of the prism

The length of the prism (the distance between the two triangular bases) is \( 16 \) in (from the diagram).

Step4: Calculate the volume

Using the volume formula for a triangular prism \( V = B \times h \), substitute \( B = 54 \) and \( h = 16 \).

$$ V=54\times16 = 864 \text{ cubic inches} $$

Answer:

The volume is \( 864 \) cubic inches.