In a regular quadrangular pyramid, the diagonal of the base is 10, and the side edge is 13. Find the volume of the pyramid.
March 20, 2021 | education
| At the base of a regular pyramid is a square, then its diagonals, at the point of their intersection, are divided in half. OA = OC = AC / 2 = 10/2 = 5 cm. From the right-angled triangle KOС, according to the Pythagorean theorem, we define the leg KO, which is the height of the pyramid.
KO ^ 2 = KC ^ 2 – OC ^ 2 = 169 – 25 = 144.
KO = 12 cm.
The base area of a square is half the products of its diagonals.
Sbn = АС ^ 2/2 = 100/2 = 50 cm2.
Then the volume of the pyramid is: V = Sosn * KO = 50 * 12 = 600 cm3.
Answer: The volume of the pyramid is 600 cm3.
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