In a regular rectangular truncated pyramid, the height is 36 cm, the apothem is 45 cm, and the sides

| May 6, 2021 | education

In a regular rectangular truncated pyramid, the height is 36 cm, the apothem is 45 cm, and the sides of the base are 1: 4, find these sides

Let the side length of the smaller base be 2 * X cm, A1D1 = 2 * X cm, then the side length of the larger base will be 8 * X cm.

The perpendiculars O1M and OK to the sides of the base are the middle lines of triangles A1C1D1 and ACD, then O1M = A1D1 / 1 = 2 * X / 2 = X cm, OK = AD / 2 = 8 * X / 2 = 4 * X cm.

Quadrangle OO1MK is a rectangular trapezoid in which we draw the height MH. KН = OK – OH = OK – O1M = 4 * X – X = 3 * X.

In a right-angled triangle MKН, but the Pythagorean theorem, MK ^ 2 = MH ^ 2 + KH ^ 2.

2025 = 1296 + 9 * X ^ 2.

9 * X ^ 2 = 729.

X ^ 2 = 81.

X = 9 cm.

Then A1D1 = 2 * 9 = 18 cm.

AD = 4 * 18 = 72 cm.

Answer: The sides of the bases of the truncated pyramid are 18 cm and 72 cm.



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