The height of a regular quadrangular pyramid is 6, the apothem of the pyramid forms an angle
| August 11, 2021 | education
The height of a regular quadrangular pyramid is 6, the apothem of the pyramid forms an angle of 30 degrees with a height. Find the area of the side surface of the pyramid
Consider a right-angled triangle OO1H, in which the leg OO1 = 6 cm, and the angle O1OH = 30.
Then tg30 = О1Н / OO1.
O1H = 6 / √3 cm.
The OH hypotenuse is the apothem of the pyramid and is equal to two lengths of the O1H leg, which lies opposite the angle of 300.
ОН = 2 * О1Н = 12 / √3 cm.
The length of the side of the base is equal to two lengths of O1H, since there is a square at the base.
AB = BC = CD = AC = 12 / √3 cm.
Sside = p * L, where p is the semiperimeter of the base, L is the apothem of the pyramid.
Sside = ((4 * 12 / √3) / 2) * 12 / √3 = 96 cm2.
Answer: S side = 96 cm2.
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