The height of a regular quadrangular pyramid is 8√3 and the angle between the planes

| September 7, 2021 | education

The height of a regular quadrangular pyramid is 8√3 and the angle between the planes of the side face and the base is 60, calculate the area of the side surface.

Since the pyramid is regular, there is a square at its base, and its side faces are isosceles triangles.

In the isosceles triangle PCD, we draw the height of the PH, which is also the median and the bisector.

In a right-angled triangle POH, according to the Pythagorean theorem, we determine the length of the leg OH.

tgРHO = PO / OH, then OH = PO / tgРHO = (8 / √3) / √3 = 8 cm.

Then, PH = 2 * OH = 2 * 8 = 16 cm, since OH lies against the angle of 30.

Since DH = CH, and AO = CO, then the OH segment is the middle line of the ACD triangle, then AD = CD = 2 * OH = 2 * 8 = 16 cm.

Determine the area of ​​the triangle СРD.

Ssrd = СD * PH / 2 = 16 * 16/2 = 128 cm2.

Then Side = 4 * Sav = 4 * 128 = 512 cm2.

Answer: The lateral surface area is 512 cm2.



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