To calculate the volume of a triangular pyramid (or tetrahedron), you can use the following formula:
\[ V = \frac{1}{3} \times B \times h \]
where:
- \( V \) is the volume of the pyramid,
- \( B \) is the area of the base,
- \( h \) is the height of the pyramid (the perpendicular distance from the base to the apex).
Since you provided only the base side length (15 cm), let's first calculate the area of the base if it is an equilateral triangle. The area \( B \) of an equilateral triangle can be calculated using the formula:
\[ B = \frac{\sqrt{3}}{4} \times a^2 \]
where \( a \) is the length of a side of the triangle.
For a base side \( a = 15 \) cm:
\[ B = \frac{\sqrt{3}}{4} \times (15)^2 \] \[ B = \frac{\sqrt{3}}{4} \times 225 \] \[ B = \frac{225\sqrt{3}}{4} \approx 97.43 \text{ cm}^2 \]
Now, you will need the height \( h \) of the pyramid to calculate the volume. Once you have the height, you can substitute back into the volume formula to find the volume of the pyramid.
Thus, the complete formula for the volume of a triangular pyramid with a triangular base of side length 15 cm is:
\[ V = \frac{1}{3} \times \left( \frac{225\sqrt{3}}{4} \right) \times h \]
In summary, you need the height \( h \) of the pyramid to calculate the final volume.