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

810 cm3
810 cm cubed

648 cm3
648 cm cubed

360 cm3
360 cm cubed

3,240 cm3

1 answer

To find the volume of the prism, we use the formula for the volume of a prism, which is:

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

First, we need to calculate the area of the parallelogram base. The area \(A\) of a parallelogram can be calculated using the formula:

\[ A = \text{Base} \times \text{Height} \]

In this case, the base measures 9 centimeters and the height (perpendicular to that base) is 4 centimeters. Therefore, the area of the parallelogram is:

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

Next, we know the height of the prism is 18 centimeters. Now, we can find the volume of the prism:

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

Thus, the volume of the prism is:

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