The height of a regular quadrangular pyramid is 16cm. The side of the base of the pyramid is 24 cm.

| February 1, 2021 | education

The height of a regular quadrangular pyramid is 16cm. The side of the base of the pyramid is 24 cm. Calculate the distance from the top of the pyramid to: a) sides of the base b) to the tops of the base

Let’s draw the AC and ВD diagonals at the base of the pyramid, with the intersection point O1.

Since the pyramid is regular, there is a square at its base, then the height of O1H, triangle DO1C, is equal to half of the side of the base of the pyramid. О1Н = DС / 2 = 24/2 = 12 cm.

Let us draw the apothem OH, and in the right-angled triangle OO1H, by the Pythagorean theorem we define the hypotenuse OH.

OH ^ 2 = OH1 ^ 2 + O1H ^ 2 = 16 ^ 2 + 12 ^ 2 = 256 + 144 = 400.

OH = 20 cm.

Consider a triangle OНС, in which the HC leg is equal to half the side of the base, since the O1H height is also the median of the DO1C triangle.

Then, by the Pythagorean theorem, we find the lateral edge of the OS.

OС ^ 2 = OH ^ 2 + HC ^ 2 = 400 + 144 = 544.

OС = 4 * √34 cm.

Answer: The distance from the top of the pyramid to the sides of the base is 20 cm. The distance from the top of the pyramid to the top of the base is 4 * √34 cm.



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