The lateral surface area of a regular triangular prism is 108 cm2. The diagonal of the side face is inclined to the plane

| September 11, 2021 | education

The lateral surface area of a regular triangular prism is 108 cm2. The diagonal of the side face is inclined to the plane of the base of the prism at an angle of 45 degrees. Find the volume of the prism

Since the prism is regular, an equilateral triangle lies at its base, and therefore, all its side faces are equal rectangles.

Then Sаа1с1с = Sbok / 3 = 108/3 = 36 cm2.

Diagonal AC1, according to the condition, is inclined to the plane of the base at an angle of 450, then triangle AA1C is rectangular and isosceles, which means AA1 = AC.

Sаа1с1с = АА1 * АС = 36 cm2.

AA1 = AC = 6 cm.

The base area is equal to: Sbase = AB * BC * Sin60 / 2 = 6 * 6 * √3 / 4 = 9 * √3 cm2.

Then V = Ssn * АА1 = 9 * √3 * 6 = 54 * √3 cm3.

Answer: The volume of the prism is 54 * √3 cm3.



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