The height of a regular quadrangular prism is H. The diagonal of the prism is with the plane

| August 9, 2021 | education

The height of a regular quadrangular prism is H. The diagonal of the prism is with the plane of the base of the angle alpha. Calculate the area of the lateral surface

In a right-angled triangle AA1C, through the leg and the acute angle, we determine the length of the leg AC.

AC = AA1 * Ctgα = H * Ctgα.

Since the pyramid is correct, there is a square at its base, AB = BC = CD = AD = a cm.

The diagonal of the square is calculated by the formula: AC = AB * √2, then AB = AC / √2 = H * Сtgα / √2 cm.

Determine the area of the side face of the prism.

S = АВ * Н = Н * Сtgα / √2 * Н = Н2 * Сtgα / √2 cm.

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

Side = 4 * S = 4 * Н ^ 2 * Сtgα / √2 = Н2 * Сtgα * 4 / √2 = 2 * √2 * Н ^ 2 * Ctgα cm2.

Answer: The area of the lateral surface of the prism is 2 * √2 * H ^ 2 * Ctgα cm2.



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