To find the volume of the prism, we first need to calculate the area of the trapezoidal base, and then use that area along with the height of the prism to determine the volume.
Step 1: Calculate the area of the trapezoidal base
The area \( A \) of a trapezoid can be calculated using the formula:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
Where:
- \( b_1 \) is the length of one base,
- \( b_2 \) is the length of the other base,
- \( h \) is the height of the trapezoid.
Given:
- \( b_1 = 4 \) cm,
- \( b_2 = 8 \) cm,
- \( h = 5 \) cm (height of the trapezoid).
Substituting the values:
\[ A = \frac{1}{2} \times (4 + 8) \times 5 \] \[ A = \frac{1}{2} \times 12 \times 5 \] \[ A = \frac{1}{2} \times 60 \] \[ A = 30 \text{ cm}^2 \]
Step 2: Volume of the prism
Now, we use the area of the base and the height of the prism to find the volume. Given that the height \( h \) of the prism is 12 cm:
\[ V = A \cdot h \] \[ V = 30 \text{ cm}^2 \cdot 12 \text{ cm} \] \[ V = 360 \text{ cm}^3 \]
Summary
- Area of the base, \( B = 30 \) cm\(^2\)
- Height of the prism, \( h = 12 \) cm
- Volume, \( V = 360 \) cm\(^3\)
Final Results
- Area of the base, \( B \): 30 cm²
- Height of the prism, \( h \): 12 cm
- Volume, \( V \): 360 cm³