In a straight triangular prism, the height is 10 m. The sides of the base are equal.

univerkov | August 16, 2021 | education

In a straight triangular prism, the height is 10 m. The sides of the base are equal. The side surface of the prism is 32 m2. Determine the total surface of the prism.

The area of the lateral surface of the prism is equal to the product of the perimeter of the base and the height of the prism.

Sside = Rosn * BB1.

Rosn = = S side / BB1 = 32/10 = 16/5 = 3.2 m.

Then the side of the base is: AB = BC = AC = (16/5) / 3 = 16/15.

Since the base is a regular triangle, then Sbase = AB ^ 2 * √3 / 4 = 256 * √3 / 225 * 4 = 64 * √3 / 225 cm2.

Then Sпов = 2 * Sсн + S side = 2 * (64 * √3 / 225) + 32 = 32 + 128 * √3 / 225 cm2.

Answer: The surface area of the prism is 32 + 128 * √3 / 225 cm2.

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