In a regular 4-sided pyramid, the height is 12 cm, and the height of the side face is 15 cm.

univerkov | June 1, 2021 | education

In a regular 4-sided pyramid, the height is 12 cm, and the height of the side face is 15 cm. Calculate the volume of the pyramid.

The height of the MO of the pyramid and the height of the ML of the lateral face form a right-angled triangle MOН, then, according to the Pythagorean theorem, OH ^ 2 = MН ^ 2 – MO ^ 2 = 225 – 144 = 81.

OH = 9 cm.

The CDM triangle is isosceles, then the height of МН is its median, and then DH = СН.

Point O is the middle of the AC diagonal, then OH is the middle line of the ACD triangle, and therefore AD = 2 * OH = 2 * 9 = 18 cm.

Let’s determine the area of the base of the pyramid. Sb = AD * CD = 18 * 18 = 324 cm2.

Then V = Sosn * MO / 3 = 324 * 12/3 = 1296 cm2.

Answer: The volume of the pyramid is 1296 cm2.

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