Calculating Right Prism Volume with Trapezium Base

The volume of any right prism is found by multiplying the area of its base by its height.

$ \text{Volume}_{\text{prism}} = \text{Area}_{\text{base}} \times \text{Height}_{\text{prism}} $

Calculating the Trapezium Base Area

The base shape is a trapezium. The formula for the area of a trapezium is:

$ \text{Area}_{\text{trapezium}} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}_{\text{trapezium}} $

Given the parallel sides are 10 cm and 6 cm, and the trapezium's height is 4 cm:

$ \text{Area}_{\text{base}} = \frac{1}{2} \times (10 \text{ cm} + 6 \text{ cm}) \times 4 \text{ cm} $

$ \text{Area}_{\text{base}} = \frac{1}{2} \times (16 \text{ cm}) \times 4 \text{ cm} $

$ \text{Area}_{\text{base}} = 8 \text{ cm} \times 4 \text{ cm} = 32 \text{ cm}^2 $

Calculating the Prism Volume

Now, use the prism volume formula with the calculated base area and the given prism height (15 cm):

$ \text{Volume}_{\text{prism}} = 32 \text{ cm}^2 \times 15 \text{ cm} $

$ \text{Volume}_{\text{prism}} = 480 \text{ cm}^3 $

Conclusion

The volume of the right prism is 480 cm$^3$.