Given a regular quadrangular pyramid SABCD, points K and P midpoints SB and SC, calculate the perimeter

| May 19, 2021 | education

Given a regular quadrangular pyramid SABCD, points K and P midpoints SB and SC, calculate the perimeter of the quadrilateral AKPD if it is known that the length of each edge of the pyramid is 6 cm.

Since the lengths of all the edges of the pyramid are equal, there is a square at the base of the pyramid, and the side faces are equilateral triangles.

The segment BP is the middle line of the triangle SBC, since points K and P are the middle of the lateral edges, then PK = CB / 2 = 6/2 = 3 cm.

Since triangles SCD and SAB are equilateral, and SK = BK and SP = CP, the segments DP and AK are the heights, medians and bisectors of the triangles.

DP = AK = 6 * √3 / 2 = 3 * √3 cm.

Let’s define the perimeter of the quadrilateral AKPD.

Rakrd = AD + AK + DP + KP = 6 + 3 * √3 + 3 * √3 + 3 = 9 + 6 * √3 cm = 3 * (3 + 2 * √3) cm.

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



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