The base of a straight prism is a regular triangle with a side equal to 10 cm

univerkov | July 13, 2021 | education

The base of a straight prism is a regular triangle with a side equal to 10 cm, and a side edge of 13 cm. Find the total surface area of a straight prism.

Since the prism is rectangular, its side faces are rectangles.

Let’s define the perimeter of the triangle ABC.

Ravs = AB + BC + AC = 10 + 10 + 10 = 30 cm.

Let us determine the area of the lateral surface of the prism.

Sside = P * AA1 = 30 * 13 = 390 cm2.

At the base of the prism there is an equilateral triangle, then Sbasn = AB ^ 2 * √3 / 4 = 100 * √3 / 4 = 25 * √3 cm2.

Then Sпов = Sbok + 2 * Sсн = 390 + 50 * √3 cm2.

Answer: The area of the prism is 390 + 50 * √3 cm2.

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