To find the volume of the prism and the pyramid, we first need to calculate the area of the triangular base.
The triangle has sides measuring 16 meters, 14 meters, and 8 meters. We can use the formula for the area of a triangle using the base and height:
Area = 1/2 × base × height
Here, the base is the side measuring 16 meters, and the height is the perpendicular distance from the opposite vertex to this base, which measures 7 meters.
Area = 1/2 × 16 m × 7 m Area = 1/2 × 112 m² Area = 56 m²
Now that we have the area of the triangular base, we can calculate the volumes of the prism and pyramid.
- Volume of the prism: The volume \( V \) of a prism is given by:
\( V = \text{Base Area} \times \text{Height} \)
In this case, the height of the prism is 15 m.
Volume of the prism = 56 m² × 15 m = 840 m³
- Volume of the pyramid: The volume \( V \) of a pyramid is given by:
\( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
Again, the height of the pyramid is also 15 m.
Volume of the pyramid = \( \frac{1}{3} \times 56 m² \times 15 m \)
Calculating this, we have:
Volume of the pyramid = \( \frac{1}{3} \times 840 m³ = 280 m³ \)
Thus, the final answers are:
- The volume of the prism is 840 m³.
- The volume of the pyramid is 280 m³.