The perimeter of the lateral face of a regular triangular prism is 20 cm.

| January 12, 2021 | education

The perimeter of the lateral face of a regular triangular prism is 20 cm. Find the area of the lateral surface of the prism if the side of its base is 4 cm.

The side face of a regular triangular prism is a rectangle, one of the sides of which is equal to the side of the base, the other is the height of the prism. The perimeter of such a side face is:
P = 2h + 2a, where h is the height of the prism and a is the side of the base.
Hence:
2h = P – 2a = 20 – 2 * 4 = 12 cm;
h = 12/2 = 6 cm – the height of the prism.
The area of ​​the side face is equal to the product of the side of the base and the height of the prism:
S = a * h = 4 * 6 = 24 cm2.
Since an equilateral triangle lies at the base of a regular triangular prism, the side faces are equal to each other. The lateral surface area is equal to the sum of the lateral face areas:
Sside = 3 * 24 = 72 cm2.



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