In a regular triangular prism, the side of the base is a, the height is h.

| June 24, 2021 | education

In a regular triangular prism, the side of the base is a, the height is h. Calculate the areas of the full and lateral surface of the prism if a = 12cm, h = 10cm.

Equilateral triangles ABC and A1B1C1 lie at the bases of the rectangular prism.

Determine the area of the base of the prism.

Sbn = АС2 * √3 / 4 = 144 * √3 / 4 = 36 * √3 cm2.

Determine the perimeter of the triangle at the base of the prism. Rosn = 3 * BC = 3 * 12 = 36 cm.

Let’s calculate the area of the lateral surface of the prism.

Sside = Rosn * AA1 = 36 * 10 = 360 cm2.

Let us determine the total surface area of the prism.

Sпов = 2 * Sсн + S side = 2 * 36 * √3 + 360 = 360 + 72 * √3 = 72 * (5 + √3) cm2.

Answer: The lateral surface area is 360 cm2, the total surface area is 72 * (5 + √3) cm2.



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