The height of a regular rectangular truncated pyramid is 14 cm, the side edge is 18 cm

| May 7, 2021 | education

The height of a regular rectangular truncated pyramid is 14 cm, the side edge is 18 cm, the diagonal is 22 cm. Find the sides of the base.

Let’s draw the diagonals АС and А1С1 at the base of the pyramid and the height А1Н. In a right-angled triangle АА1Н, we define, according to the Pythagorean theorem, the length of the leg АН.

AH ^ 2 = AA1 ^ 2 – A1H ^ 2 = 18 ^ 2 – 14 ^ 2 = 324 – 196 = 128.

AH = 8 * √2 cm.

From the right-angled triangle CHA1, by the Pythagorean theorem, we determine the length of the leg OC.

OH ^ 2 = CA1 – A1H ^ 2 = 22 ^ 2 – 14 ^ 2 = 484 – 196 = 288.

OH = 12 * √2 cm.

Then the diagonal of the base AC = AH + CH = 8 * √2 + 12 * √2 = 20 * √2 cm.

Determine the length of the diagonal of the smaller base.

A1C1 = (AC – 2 * AH) = 20 * √2 – 16 * √2 = 4 * √2 cm.

ABCD – square, the diagonal of the square to the product of the side and the square root of two

(d = a * √2), then АD = АС / √2 = 20 * √2 / √2 = 20 cm.

Similarly, A1D1 = A1C1 / √2 = 4 * √2 / √2 = 4 cm.

Answer: The sides of the bases of the truncated pyramid are 20 cm and 4 cm.



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