The base of the pyramid is a rhombus with diagonals of 30 cm and 40 cm. The tops of the pyramid are removed

| September 3, 2021 | education

The base of the pyramid is a rhombus with diagonals of 30 cm and 40 cm. The tops of the pyramid are removed with the sides of the base by 13 cm. Find the height of the pyramid.

Since there is a rhombus at the base of the pyramid, its diagonals, at the point of their intersection, are divided in half and intersect at right angles.

Then О = ВD / 2 = 30/2 = 15 cm, OC = АС / 2 = 40/2 = 20 cm.

In a right-angled triangle COD, according to the Pythagorean theorem, CD ^ 2 = OD ^ 2 + OC ^ 2 = 225 + 400 = 625.

СD = 25 cm.

Determine the area of the triangle OD. Sod = OD * OC / 2 = 15 * 20/2 = 150 cm2.

Also Scod = OH * CD / 2.

OH = 2 * Sod / CD = 2 * 150/25 = 12 cm.

In a right-angled triangle POH, according to the Pythagorean theorem, we determine the length of the leg OP.

OR ^ 2 = PH ^ 2 – OH ^ 2 = 169 – 144 = 25.

OR = 5 cm.

Answer: The height of the pyramid is 5 cm.



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