In a regular quadrangular pyramid, the height is 3 and the apothem is 5. Find the distance

| February 25, 2021 | education

In a regular quadrangular pyramid, the height is 3 and the apothem is 5. Find the distance from the center of the base to the side face.

Triangle SOH is rectangular, then, according to the Pythagorean theorem, we determine the length of the leg OH.

OH ^ 2 = SH ^ 2 – SO ^ 2 = 25 – 9 = 16.

OH = 4 cm.

Consider right-angled triangles ОМS and ОМН, which have a common leg ОМ.

Let the segment MH = X cm, then SM = (5 – X) cm.

In a right-angled triangle OMН, OM ^ 2 = OH ^ 2 – MH ^ 2 = 16 – X2. (one).

In a right-angled triangle SOM, OM ^ 2 = SO ^ 2 – SM ^ 2 = 9 – (5 – X) ^ 2. (2).

Equate Equations 1 and 2.

16 – X ^ 2 = 9 – 25 + 10 * X – X ^ 2.

10 * X = 32.

X = MH = 3.2 cm.

Then OM ^ 2 = 16 – 10.24 = 5.76.

OM = 2.4 cm.

Answer: The distance from the center of the base to the side edge is 2.4 cm



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