Calculate the volume of a quadrangular pyramid, at the base of which there is a rectangle

| May 9, 2021 | education

Calculate the volume of a quadrangular pyramid, at the base of which there is a rectangle with sides 15 and 20, and the side edge is 25.

From the right-angled triangle ACD, by the Pythagorean theorem, we define the hypotenuse AC, which is the diagonal of the rectangle.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 20 ^ 2 + 15 ^ 2 = 400 + 225 = 625.

AC = 25 cm.

Since the length of the lateral rib coincides with the length of the diagonal of the base, SC = SA = AC = 25 cm, the triangle SAC is equilateral. The height of an equilateral triangle is determined by the formula:

SO = SC * √3 / 2 = 25 * √ 3/2 cm.

Determine the area of the base of the pyramid.

Sb = AD * CD = 20 * 15 = 300 cm2.

Let’s define the volume of the pyramid.

V = Sn * SO / 3 = (300 * 25 * √ 3/2) / 3 = 1250 * √ 3 cm3.

Answer: The volume of the pyramid is 1250 * √ 3 cm3.



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