Given a pyramid, the base of which is a rectangle, and the top is projected at the point of intersection of the diagonals

| April 9, 2021 | education

Given a pyramid, the base of which is a rectangle, and the top is projected at the point of intersection of the diagonals of the base. All side edges of the pyramid are 13 cm, and the height is 12 cm. One side of the base of the pyramid is 8 cm. Find the other side of the base.

Since the top of the pyramid K is projected into the point of intersection of the diagonals of the base of the pyramid, the triangle KOC is rectangular, from which we determine the size of the leg OC using the Pythagorean theorem.

OC ^ 2 = KC ^ 2 – KO ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25.

OC = 5 cm.

Since there is a rectangle at the base of the pyramid, the length of the diagonal AC = OC * 2 = 5 * 2 = 10 cm, since the diagonals are divided in half at the point of their intersection.

In a right-angled triangle ACD, we determine the length of the AC leg.

CD ^ 2 = AC ^ 2 – AD ^ 2 = 10 ^ 2 – 8 ^ 2 = 100 – 64 = 36.

CD = 6 cm.

Answer: The second moan of the base is 6 cm.



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