In a regular 4-sided pyramid SABCD, the side of the square ABCD lying at the base is √2

| February 15, 2021 | education

In a regular 4-sided pyramid SABCD, the side of the square ABCD lying at the base is √2, and the height lowered to the base is 2. Find. distance from point A to plane SBC.

Let’s draw a straight line KM through point O, parallel to AB, as well as the height SM of an isosceles triangle SBC. The perpendicular KH to the height SM is our desired distance.

KM = AB = √2 cm. Point O divides the segment KM in half, then MO = KM / 2 = √2 / 2 cm.

The SOM triangle is rectangular, then SM ^ 2 = SO ^ 2 + OM ^ 2 = 4 + 2/4 = 18/4 = 9/2.

SM = 3 / √2 cm.

Determine the area of the triangle SКМ.

Sskm = SO * KM / 2 = 2 * √2 / 2 = √2 cm2.

Also, the area of the triangle SKM is:

Sskm = SM * KН / 2.

KN = 2 * Sskm / SM = 2 * √2 / (3 / √2) = 4/3 = 1 (1/3) cm.

Answer: The distance from point A to the plane SBC is 1 (1/3) cm.



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