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To find the volume of the greenhouse, which is shaped like a prism, we need to calculate the volume of the prism by determining the area of its cross-sectional shape and multiplying it by its length.

### Step-by-Step Calculation:

1. **Determine the shape of the cross-section:**
   The cross-section of the greenhouse is a composite shape made up of:
   - A rectangle at the bottom
   - A trapezoid on top

   **Dimensions of the cross-section:**
   - The rectangular part has a height of \(1.6 \, m\) and a width of \(3.2 \, m\) (since \(1.6 \, m + 1.6 \, m = 3.2 \, m\)).
   - The trapezoidal part has a height of \(0.8 \, m\), a top width of \(1.6 \, m\), and a bottom width of \(3.2 \, m\).

2. **Calculate the area of the rectangular part:**
   \[
   \text{Area of the rectangle} = \text{height} \times \text{width} = 1.6 \, m \times 3.2 \, m = 5.12 \, m^2
   \]

3. **Calculate the area of the trapezoidal part:**
   The formula for the area of a trapezoid is:
   \[
   \text{Area of the trapezoid} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
   \]
   Substituting the values:
   \[
   \text{Area of the trapezoid} = \frac{1}{2} \times (3.2 \, m + 1.6 \, m) \times 0.8 \, m = \frac{1}{2} \times 4.8 \, m \times 0.8 \, m = 1.92 \, m^2
   \]

4. **Calculate the total cross-sectional area:**
   \[
   \text{Total cross-sectional area} = \text{Area of rectangle} + \text{Area of trapezoid} = 5.12 \, m^2 + 1.92 \, m^2 = 7.04 \, m^2
   \]

5. **Calculate the volume of the greenhouse:**
   The volume of the prism is given by:
   \[
   \text{Volume} = \text{Cross-sectional area} \times \text{Length}
   \]
   The length of the greenhouse is \(19 \, m\). Therefore:
   \[
   \text{Volume} = 7.04 \, m^2 \times 19 \, m = 133.76 \, m^3
   \]

6. **Round to the nearest cubic meter:**
   \[
   V \approx 134 \, m^3
   \]

### Final Answer:
The volume of the greenhouse is **134 cubic meters**.

Would you like more details or have any questions?

Here are 5 related questions you might be interested in:
1. How do you calculate the volume of a prism with different cross-sections?
2. What are the properties of composite shapes in geometry?
3. How do you find the area of irregular shapes?
4. What are some real-life applications of calculating volumes of prisms?
5. How do changes in dimensions affect the volume of a shape?

**Tip:** Always break down composite shapes into simpler geometric figures to calculate their areas or volumes accurately.

Work out the volume of a commercial greenhouse that is shaped like a prism, with given dimensions including a rectangular and trapezoidal cross-section.

Learn how to calculate the volume of a commercial greenhouse shaped like a prism. This problem involves calculating the area of composite shapes (rectangle and trapezoid) and using the formula for the volume of a prism. Perfect for students in Grades 8-10.

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