1. **State the problem:** We need to find the volume of a composite solid consisting of a rectangular prism base and two triangular prisms on top. 2. **Identify the shapes and dimensions:** - Rectangular prism base: length $25$ cm, height $5$ cm, width (not given explicitly, but assumed to be the same as the base of the triangular prisms) $12.5$ cm. - Two triangular prisms on top: each has a base length $12.5$ cm, height $7.5$ cm, and the same width as the rectangular prism $25$ cm. 3. **Volume formulas:** - Volume of rectangular prism: $$V_{rect} = \text{length} \times \text{width} \times \text{height}$$ - Volume of triangular prism: $$V_{tri} = \frac{1}{2} \times \text{base} \times \text{height} \times \text{length}$$ 4. **Calculate the volume of the rectangular prism:** $$V_{rect} = 25 \times 12.5 \times 5 = 1562.5 \text{ cm}^3$$ 5. **Calculate the volume of one triangular prism:** $$V_{tri} = \frac{1}{2} \times 12.5 \times 7.5 \times 25$$ $$= \frac{1}{2} \times 12.5 \times 7.5 \times 25 = 1171.875 \text{ cm}^3$$ 6. **Calculate the volume of two triangular prisms:** $$2 \times 1171.875 = 2343.75 \text{ cm}^3$$ 7. **Calculate the total volume:** $$V_{total} = V_{rect} + 2 \times V_{tri} = 1562.5 + 2343.75 = 3906.25 \text{ cm}^3$$ 8. **Round to the nearest hundredth:** $$\boxed{3906.25 \text{ cm}^3}$$