To calculate the volume of the given composite solid, we will split the shape into two parts:

1. Rectangular Prism (Base)
   Dimensions: Length $5 \, \text{cm}$, Width $2 \, \text{cm}$, Height $2 \, \text{cm}$.

2. Triangular Prism (Top)
   The triangular face has a base of $5 \, \text{cm}$, height of $3 \, \text{cm}$, and the length/depth of the prism is $2 \, \text{cm}$.

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Step 1: Volume of the Rectangular Prism

$\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$ $\text{Volume} = 5 \times 2 \times 2 = 20 \, \text{cm}^3$

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Step 2: Volume of the Triangular Prism

$\text{Volume} = \frac{1}{2} \times \text{Base} \times \text{Height} \times \text{Depth}$ $\text{Volume} = \frac{1}{2} \times 5 \times 3 \times 2 = \frac{1}{2} \times 30 = 15 \, \text{cm}^3$

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Step 3: Total Volume of the Composite Solid

$\text{Total Volume} = \text{Volume of Rectangular Prism} + \text{Volume of Triangular Prism}$ $\text{Total Volume} = 20 + 15 = 35 \, \text{cm}^3$

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Final Answer:

The volume of the composite solid is: $\boxed{35 \, \text{cm}^3}$

Would you like a detailed breakdown of the calculation steps or have further questions?

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Related Questions:

1. How is the surface area of the composite solid calculated?
2. What is the significance of splitting the figure into basic shapes for calculations?
3. Can you calculate the diagonal length of the rectangular prism base?
4. How does the height of the triangular prism affect the total volume?
5. How can you use this method for irregularly shaped solids?

Tip:

For composite shapes, always break them into simpler shapes with known formulas to ensure accuracy.