At the base of the straight prism lies a regular triangle with a side of 5 cm. The straight line passing through the middle

| September 16, 2021 | education

At the base of the straight prism lies a regular triangle with a side of 5 cm. The straight line passing through the middle of the side of the lower base and the opposite apex of the upper base is inclined to the plane of the base at an angle of 45 degrees. Find the volume of a prism

At the base of the prism lies an equilateral triangle ABC with a side of 5 cm.

Then its area will be equal to: Sax = AC ^ 2 * √3 / 4 = 25 * √3 / 4 cm2.

Let’s draw the height АН of the triangle ABC, the length of which is equal to: АН = ВС * √3 / 2 = 5 * √3 / 2 cm.

Triangle АА1Н is rectangular, in which the angle АНН1 = 450, then the leg АА1 = АН = 5 * √3 / 2 cm.

Let’s define the volume of the prism.

V = Sbase * АА1 = (25 * √3 / 4) * (5 * √3 / 2) = 375/8 = 46 (7/8) cm3.

Answer: The volume of the prism is 46 (7/8) cm3.



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