In a regular quadrangular pyramid, the side of the base is 12 cm and the apothem is 15 cm.

univerkov | August 22, 2021 | education

In a regular quadrangular pyramid, the side of the base is 12 cm and the apothem is 15 cm. Find the side edge of the pyramid.

Since the apothem is the height of the lateral face of the pyramid, and the lateral face of the pyramid is an isosceles triangle, apothem P is also the median of the BCP triangle.

Then ВН = СН = ВС / 2 = 12/2 = 6 cm.

From the right-angled triangle PBH, we determine the length of the hypotenuse PB, which is the lateral edge of the pyramid.

PB ^ 2 = PH ^ 2 + BH ^ 2 = 225 + 36 = 261.

PB = 3 * √29 cm.

Answer: The length of the side rib is 3 * √29 cm.

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