In a regular quadrangular pyramid, the side of the base is 10 cm, the side face is inclined to the plane of the base at an angle

| September 2, 2021 | education

In a regular quadrangular pyramid, the side of the base is 10 cm, the side face is inclined to the plane of the base at an angle of 60 degrees. Find: The area of the side surface of the pyramid.

The side faces of the pyramid are isosceles triangles.

Let’s build the height of the PH, which is also 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 = 10/2 = 5 cm.

In a right-angled triangle POH, the angle OPH = (90 – 60) = 30, then the leg OH, which lies opposite this angle, is two times shorter than the hypotenuse of the PH. Then PH = 2 * 5 = 10 cm.

Determine the area of the triangle PCD.

Sрсд = СD * PН / 2 = 10 * 10/2 = 50cm2.

Then S side = 4 * Srcd = 4 * 50 = 200 cm2.

Answer: The lateral surface area is 200 cm2.



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