The side of the base of a regular quadrangular pyramid is 2 cm. The side edges are inclined to the base plane at an angle

| March 13, 2021 | education

The side of the base of a regular quadrangular pyramid is 2 cm. The side edges are inclined to the base plane at an angle of 45 degrees. Find the volume of the pyramid.

Determine the area of ​​the base of the pyramid. Sbn = AB ^ 2 = 2 ^ 2 = 4 cm2.

Since the pyramid is regular, there is a square at its base, and all the side edges are equal.

In a right-angled triangle ACD, AD = CD = 2 cm.

Then, by the Pythagorean theorem, AC ^ 2 = 2 * AD ^ 2 = 2 * 4 = 8.

AC = 2 * √2 cm.

The diagonals of the square are equal and the point of their intersection is divided in half, then CO = AC / 2 = 2 * √2 / 2 = √2 cm.

In a right-angled triangle KOC, the angle OCK = 450, then the triangle KOC is rectangular and isosceles, OK = OC = √2 cm.

Let’s define the volume of the pyramid.

V = Sbn * OK / 3 = 4 * √2 / 3 cm3.

Answer: The volume of the pyramid is 4 * √2 / 3 cm3.



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