I'm studying for my geometry exam and I'm having trouble finding the volume of a right rectangular pyramid. The pyramid has a height of 15 units and a base with length and width of 10 units and 12 units, respectively. Can you find the solution to this problem?

Answer 1

To find the volume of a right rectangular pyramid, you can use the following formula:

\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

1. Calculate the base area of the rectangular base. The base area \( A \) can be found using the formula for the area of a rectangle:

\[ A = \text{length} \times \text{width} \]

In this case, the length is 10 units, and the width is 12 units.

\[ A = 10 \times 12 = 120 \text{ square units} \]

2. Plug the base area and height into the volume formula. The height of the pyramid is given as 15 units.

\[ \text{Volume} = \frac{1}{3} \times 120 \times 15 \]

3. Calculate the volume:

\[ \text{Volume} = \frac{1}{3} \times 120 \times 15 = \frac{1}{3} \times 1800 = 600 \text{ cubic units} \]

So, the volume of the right rectangular pyramid is \( \boxed{600} \) cubic units.