The base of a right prism is a trapezium whose lengths of two parallel sides are 10 cm and 6 cm and distance between them is 5 cm. If the height of the prism is 8 cm, its volume is

Options

A. `320 cm^(3)`
B. `300.5 cm^(3)`
C. `310 cm^(3)`
D. `300 cm^(3)`

Answer

To find the volume of the right prism with a trapezium as its base, we can follow these steps:

### Step 1: Calculate the Area of the Trapezium
The formula for the area of a trapezium (trapezoid) is given by:

\[ \text{Area} = \frac{(l_1 + l_2) \times d}{2} \]

Where:
- \( l_1 \) = length of the first parallel side = 10 cm
- \( l_2 \) = length of the second parallel side = 6 cm
- \( d \) = distance between the parallel sides = 5 cm

Substituting the values into the formula:

\[ \text{Area} = \frac{(10 + 6) \times 5}{2} \]

Calculating the sum of the lengths of the parallel sides:

\[ 10 + 6 = 16 \]

Now substituting back into the area formula:

\[ \text{Area} = \frac{16 \times 5}{2} = \frac{80}{2} = 40 \text{ cm}^2 \]

### Step 2: Calculate the Volume of the Prism
The volume \( V \) of a prism is calculated using the formula:

\[ V = \text{Base Area} \times \text{Height} \]

Where:
- Base Area = 40 cm² (calculated in Step 1)
- Height = 8 cm

Substituting the values into the formula:

\[ V = 40 \times 8 = 320 \text{ cm}^3 \]

### Final Answer
The volume of the right prism is \( 320 \text{ cm}^3 \).

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