To find the volumes of the prism and the pyramid, we need to first calculate the area of the triangular base.
The formula for the area \( A \) of a triangle can be given as:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, we'll take the base of the triangle to be the side measuring 16 meters, and the height is given as 7 meters.
So, the area of the triangular base is:
\[ A = \frac{1}{2} \times 16 , \text{m} \times 7 , \text{m} = \frac{1}{2} \times 112 , \text{m}^2 = 56 , \text{m}^2 \]
Volume of the Prism
The volume \( V \) of a prism is given by:
\[ V = \text{Base Area} \times \text{Height} \]
Substituting the values we have:
\[ V = 56 , \text{m}^2 \times 15 , \text{m} = 840 , \text{m}^3 \]
Volume of the Pyramid
The volume \( V \) of a pyramid is given by:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Substituting the values we have:
\[ V = \frac{1}{3} \times 56 , \text{m}^2 \times 15 , \text{m} = \frac{1}{3} \times 840 , \text{m}^3 = 280 , \text{m}^3 \]
Final Answers
- The volume of the prism is \( 840 , \text{m}^3 \).
- The volume of the pyramid is \( 280 , \text{m}^3 \).