The base of a straight prism is a rhombus with an angle of 60. The smaller of the two sections of the prism

univerkov | September 4, 2021 | education

The base of a straight prism is a rhombus with an angle of 60. The smaller of the two sections of the prism that pass through pairs of side edges that do not belong to the same face is a square whose area is 9. Find the area of the base of the prism.

Since the smaller section BB1D1D is a square with an area of 9 cm2, then BB1 = B1D1 = D1D = BD = √Sq = √9 = 3 cm.

Consider a triangle ABD in which AB = AD as the sides of a rhombus, the angle BAD = 60 by condition, then triangle ABD is equilateral, AB = BD = AD = 3 cm.

Then the area of the rhombus in the base of the prism will be equal to: Sbase = AB * AD * SinBAD = 3 * 3 * Sin60 = 9 * √3 / 2 cm2.

Answer: The area of the base of the prism is 9 * √3 / 2 cm2.

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