Subjects geometry

Prism Volume Af846E

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1. **State the problem:** We need to find the volume of a prism whose cross section is a parallelogram. The parallelogram has one pair of opposite sides 8 cm long and the distance (height) between these sides is 4 cm. The length (or height) of the prism is 1.2 cm. 2. **Formula for volume of a prism:** The volume $V$ of a prism is given by: $$V = \text{Area of cross section} \times \text{length of prism}$$ 3. **Area of the parallelogram:** The area $A$ of a parallelogram is: $$A = \text{base} \times \text{height}$$ Here, base = 8 cm and height = 4 cm. 4. **Calculate the area:** $$A = 8 \times 4 = 32 \text{ cm}^2$$ 5. **Calculate the volume:** Using the length of the prism $l = 1.2$ cm, $$V = 32 \times 1.2 = 38.4 \text{ cm}^3$$ **Final answer:** The volume of the prism is $38.4$ cubic centimeters.