The base side of a regular triangular prism is a, the side edge is b, find the total surface area of the prism.
| September 14, 2021 | education
In a regular prism, at the base lies an equilateral triangle AB = BC = AC = a cm, and its lateral faces are rectangles with sides a and b.
Let us determine the area of the lateral surface of the prism.
Sside = P * h, where P is the perimeter of the triangle at the base, h is the height of the prism, it is also the height of the side face. Sside = 3 * a * b cm2.
The area of the base of the prism is calculated by the formula for the area of an equilateral triangle: Sbn = a ^ 2 * √3 / 4 cm2.
Determine the total surface area of the prism.
S floor = S side + 2 * S main = 3 * a * b + 2 * a ^ 2 * √3 / 4 = 3 * a * b + a ^ 2 * √3 / 2 cm2.
Answer: The total surface area is 3 * a * b + a ^ 2 * √3 / 2 cm2.
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