In a regular quadrangular pyramid with a base side of 8 cm, the side face is inclined to the base plane at an angle

| June 3, 2021 | education

In a regular quadrangular pyramid with a base side of 8 cm, the side face is inclined to the base plane at an angle of 60 degrees. Find: A) the height of the pyramid B) the area of the lateral surface.

The side faces of the pyramid are isosceles triangles.

Let’s construct the height of the PH, which will also be the median of the triangle CDP. Point O divides the diagonal AC in half, then OH is the middle line of the triangle ACD, and then OH = AD / 2 = 8/2 = 4 cm.

In a right-angled triangle, POH tg60 = PO / OH.

PO = OH * tg60 = 4 * √3cm. Then PH ^ 2 = PO ^ 2 + OH ^ 2 = 48 + 16 = 64. PH = 8 cm.

Determine the area of the triangle PCD.

Sрсд = СD * РH / 2 = 8 * 8/2 = 32cm2.

Then S side = 4 * Srcd = 4 * 32 = 128 cm2.

Answer: The height of the pyramid is 4 * √3 cm, the side area is 128 cm2.



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