The lateral edge of a regular triangular prism is 4 times the side of the base, and the sum

| March 8, 2021 | education

The lateral edge of a regular triangular prism is 4 times the side of the base, and the sum of all edges is 36. Find the total surface area of the prism.

Let the length of the side of the triangle at the base of the prism be equal to X cm, then the length of the side edge will be equal to 4 * X cm.

Then the sum of the lengths of all the edges of the prism will be: 6 * X + 3 * 4 * X = 36.

18 * X = 36.

X = AB = BC = AC = 36/18 = 2 cm.

Then AA1 = BB1 = CC1 = 4 * 2 = 8 cm.

Determine the area of the base of the prism, which is a regular triangle.

Savs = AB ^ 2 * √3 / 4 = 4 * √ 3/4 = √3 cm2.

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

Side = 3 * AB * AA1 = 3 * 2 * 8 = 48 cm2.

Let us determine the total surface area of the prism.

S floor = 2 * S main + S side = 2 * √3 + 48 cm2.

Answer: The total area of the prism is 2 * √3 + 48 cm2.



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