Calculate c Incl. The volume of the solid. Total surface area

Let the unknown side be $x$. Using the Pythagorean theorem for the right-angled base triangle:

$$7^2 + x^2 = 25^2$$ $$49 + x^2 = 625$$ $$x^2 = 625 - 49$$ $$x^2 = 576$$ $$x = \sqrt{576}$$ $$x = 24 \text{ cm}$$

The unknown side of the triangular base is 24 cm.

The area of a right-angled triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.

$$\text{Area of base} = \frac{1}{2} \times 7 \text{ cm} \times 24 \text{ cm}$$ $$\text{Area of base} = \frac{1}{2} \times 168 \text{ cm}^2$$ $$\text{Area of base} = 84 \text{ cm}^2$$

The volume of a prism is given by the formula: $\text{Volume} = \text{Area of base} \times \text{Height of prism}$.

$$\text{Volume} = 84 \text{ cm}^2 \times 10 \text{ cm}$$ $$\text{Volume} = 840 \text{ cm}^3$$

The volume of the solid is $\boxed{\text{840 cm}^3}$.

The perimeter of the base is the sum of its three sides.

$$\text{Perimeter of base} = 7 \text{ cm} + 24 \text{ cm} + 25 \text{ cm}$$ $$\text{Perimeter of base} = 56 \text{ cm}$$

The total surface area of a prism is given by the formula: $\text{Total Surface Area} = 2 \times \text{Area of base} + \text{Perimeter of base} \times \text{Height of prism}$.

$$\text{Total Surface Area} = 2 \times 84 \text{ cm}^2 + 56 \text{ cm} \times 10 \text{ cm}$$ $$\text{Total Surface Area} = 168 \text{ cm}^2 + 560 \text{ cm}^2$$ $$\text{Total Surface Area} = 728 \text{ cm}^2$$

The total surface area of the solid is $\boxed{\text{728 cm}^2}$.