1. **Stating the problem:** We have a tetrahedron with a triangular base. The base triangle has sides 7 cm and 5 cm, and the height from the base to the apex (top vertex) is 13 cm. We want to understand or calculate properties related to this tetrahedron. 2. **Formula for volume of a tetrahedron:** The volume $V$ of a tetrahedron is given by $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ where the height is the perpendicular distance from the base to the apex. 3. **Finding the base area:** Since only two sides of the base triangle are given (7 cm and 5 cm), we need the angle between them or the third side to find the area exactly. If we assume the base is a right triangle with legs 7 cm and 5 cm (common assumption if no angle given), then the area $A$ is $$A = \frac{1}{2} \times 7 \times 5 = \frac{35}{2} = 17.5 \text{ cm}^2$$ 4. **Calculating the volume:** Using the height $h = 13$ cm, $$V = \frac{1}{3} \times 17.5 \times 13 = \frac{1}{3} \times 227.5 = 75.8333... \text{ cm}^3$$ 5. **Final answer:** The volume of the tetrahedron is approximately $$\boxed{75.83 \text{ cm}^3}$$ This calculation assumes the base triangle is right angled between the sides 7 cm and 5 cm. If the angle or third side is different, the base area and volume will change accordingly.