In a regular 4x angle pyramid, the height is 12 cm, and the height of the side edge is 15 cm.

| May 2, 2021 | education

In a regular 4x angle pyramid, the height is 12 cm, and the height of the side edge is 15 cm. Find the volume 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, which are in half at the point of their intersection. Let’s connect the point of intersection of the diagonals O with the point H. The segment OH is the middle line of the triangle ACD since point O is the middle of the diagonal AC, point H is the middle of the side CD.

From the right-angled triangle KOH, we determine, by the Pythagorean theorem, the length of the leg OH.

OH ^ 2 = KH ^ 2 – KO ^ 2 = 225 – 144 = 81.

OH = 9 cm.

Then AD = 2 * OH = 2 * 9 = 18 cm.

Determine the area of ​​the base of the pyramid. Sbn = АD ^ 2 = 18 ^ 2 = 324 cm2.

Let’s define the volume of the pyramid. V = Sosn * KO / 3 = 324 * 12/3 = 1296 cm3.

Answer: The volume of the pyramid is 1296 cm3.



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