The base of the pyramid is a rectangle with sides of 12 and 16 cm. The height of the pyramid is 8 and passes through

| August 3, 2021 | education

The base of the pyramid is a rectangle with sides of 12 and 16 cm. The height of the pyramid is 8 and passes through the point of intersection of the base diagonals. Find the side edges of the pyramid.

Since there is a rectangle at the base of the pyramid, its diagonals are equal and are halved at the point of their intersection. АС = ВD, ОА = ОВ = OC = ОD = АС / 2.

In a right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 256 + 144 = 400.

AC = BD = 20 cm.

Then OC = OD = AC / 2 = 20/2 = 10 cm.

In the right-angled triangle OCK, by the Pythagorean theorem, we determine the length of the hypotenuse CK.

CK ^ 2 = OK ^ 2 + OC ^ 2 = 64 + 100 = 164.

CK = 2 * √41 cm.

Since the height of the pyramid is projected to the point of intersection of the diagonals, the lengths of the side edges are equal.

AK = BK = CK = DK = 2 * √41 cm.

Answer: The side edges of the pyramid are 2 * √41 cm.



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