A prism with parallelogram bases has a height of 18 centimeters. The adjacent sides of the parallelogram measure 5 centimeters and 9 centimeters, and the height of the parallelogram, perpendicular to the 9 centimeter side, is 4 centimeters. Find the volume of the prism.(1 point)

Responses

648 cm3
648 cm cubed

810 cm3
810 cm cubed

3,240 cm3
3,240 cm cubed

360 cm3

1 answer

To find the volume of the prism, we can use the formula:

\[ \text{Volume} = \text{Base Area} \times \text{Height} \]

First, we need to calculate the area of the parallelogram base.

The area \(A\) of a parallelogram is given by:

\[ A = \text{base} \times \text{height} \]

In this case, the base of the parallelogram is 9 cm, and the height (perpendicular to that base) is 4 cm. Thus, we can calculate the area as follows:

\[ A = 9 , \text{cm} \times 4 , \text{cm} = 36 , \text{cm}^2 \]

Next, we can calculate the volume of the prism using the area of the base and the height of the prism (18 cm):

\[ \text{Volume} = 36 , \text{cm}^2 \times 18 , \text{cm} = 648 , \text{cm}^3 \]

Therefore, the volume of the prism is:

\[ \boxed{648 , \text{cm}^3} \]