The height of a regular quadrangular pyramid is equal to the root of 6 cm, and the lateral

univerkov | June 11, 2021 | education

The height of a regular quadrangular pyramid is equal to the root of 6 cm, and the lateral rib is inclined to the plane of the base at an angle of 60 degrees. Find the lateral rib of the pyramid.

Since the pyramid is correct, the square ABCD lies at its base. Let’s draw the diagonals AC and BD of the square. The height PO of the pyramid passes through the point O, then the triangle POC is rectangular, in which we determine the length of the hypotenuse PC.

SinPCO = PO / PC.

PC = PO / SinРСO = √6 / Sin60 = √6 / (√3 / 2) = 2 * √2 cm.

Answer: The side edge of the pyramid is 2 * √2 cm.

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