The apothem of a regular triangular pyramid is l, and the dihedral angle at the base edge is α.

| August 22, 2021 | education

The apothem of a regular triangular pyramid is l, and the dihedral angle at the base edge is α. Find the area of the side surface of the pyramid.

In a right-angled triangle DOH, the linear angle OHD = α, since it is equal to the dihedral angle between the side edge and the base. Then Cosα = OH / DH.

OH = DH * Cosα = L * Cosα see.

By the property of the medians of the triangle OA = 2 * OH = 2 * L * Cosα cm, then AH = OA + OH = 3 * L * Cosα cm.

AH is the height of an equilateral triangle ABC, then AH = BC * √3 / 2.

ВС = 2 * АН / √3 = 2 * 3 * L * Cosα / √3 = 2 * √3 * L * Cosα see.

Determine the area of the side face of the pyramid. Ssvd = ВС * DH / 2 = 2 * √3 * L * Cosα * L / 2 = √3 * L2 * Cosα cm2.

Answer: The lateral surface area is √3 * L2 * Cosα cm2.



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