In an inclined prism, the side edge is 7 cm, the perpendicular section is a right-angled triangle with legs: 4 cm and 3 cm. Find the volume of the prism.
By condition, section A1MK is perpendicular to the side face of CC1B1K.
Since the perpendicular section is a right-angled triangle, its area will be equal to:
Ssection = A1M * MK / 2 = 4 * 3/2 = 6 cm2.
The volume of the inclined prism is equal to the product of the area of the perpendicular section by the length of the lateral rib, then:
Vpr = Ssech * CC1 = 6 * 7 = 42 cm3.
Answer: The volume of the prism is 42 cm3.
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