In a regular quadrangular pyramid, the side of the base is 6 cm, and the angle of inclination of the side face

| January 31, 2021 | education

In a regular quadrangular pyramid, the side of the base is 6 cm, and the angle of inclination of the side face to the plane of the base is 60 degrees. Find the side edge of the pyramid.

The side faces of the pyramid are isosceles triangles.

Let’s construct the height of the РН, which will also be the median of the SDR triangle. Point O divides the AC diagonal in half, then OH is the middle line of the AСD triangle, and then OH = AD / 2 = 6/2 = 3 cm.

In a right-angled triangle РOН, the angle OРН = (90 – 60) = 300, then the OH leg located opposite it is two times shorter than the hypotenuse of the RН. Then PH = 2 * OH = 2 * 3 = 6 cm.

From the right-angled triangle DНР, according to the Pythagorean theorem, RD^2 = DН^2 + PH^2 = 9 * 36 = 45.

РD = 3 * √5 cm.

Answer: The length of the side rib is 3 * √5 cm.



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