The lateral edge of the inclined quadrangular prism is 12, and the perpendicular section is a rhombus
| March 17, 2021 | education
The lateral edge of the inclined quadrangular prism is 12, and the perpendicular section is a rhombus with a side of 6 and an angle of 30 degrees. Find the volume of the prism.
Let us determine the area of the perpendicular section of the prism, which is the НKСD rhombus.
Ssection = НK * НD * Sin30 = 6 * 6 * 1/2 = 18 cm2.
The volume of the inclined prism is equal to the product of the length of its lateral edge by the area of the perpendicular section.
V = AA1 * Ssection = 12 * 18 = 216 cm3.
Answer: The volume of the prism is 216 cm3.
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