SABCD is a regular quadrangular pyramid, each edge of which is 6 cm long. Point O is the midpoint of the edge BC

| July 18, 2021 | education

SABCD is a regular quadrangular pyramid, each edge of which is 6 cm long. Point O is the midpoint of the edge BC of the pyramid. Construct a section of the pyramid with a plane that passes through line SO and parallel to line BD. Calculate the perimeter of this section.

Since point O is the midpoint of the segment BC, SO is the median of triangle SBC, and since the pyramid is regular, its side faces are isosceles triangles, and therefore SO is the height of triangle SBC. Then, by the Pythagorean theorem, SO ^ 2 = SC ^ 2 – CO ^ 2 = 36 – 9 = 27.

SO = 3 * √3 cm.

At the base of the pyramid lies a square with a side of cm, then its diagonal BD = DC * √2 = 6 * √2 cm.

Let’s draw a segment OH, parallel to BD, then the isosceles triangle SOH is the required section. In the BCD triangle, the OH segment is its middle line, then OH = BD / 2 = 3 * √2 cm.

Determine the perimeter of the section.

Pson = 2 * SO + OH = 2 * 3 * √3 + 3 * √2 = 3 * (2 * √3 + √2) see.

Answer: The perimeter of the section is 3 * (2 * √3 + √2) cm.



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