FABC is a pyramid. M, N and K are the midpoints of AF, FC and AB. Construct a section of the pyramid with

| August 23, 2021 | education

FABC is a pyramid. M, N and K are the midpoints of AF, FC and AB. Construct a section of the pyramid with a plane (MNK) Find the perimeter of the section if AC = 8 cm, BF = 6 cm

Since the points M, N and K are the midpoints of the edges AF, FC and AB, the segment MN is the midline of the side face AFC, KM is the midline of the face AFB. Then MN = AC / 2 = 8/2 = 4 cm, MK = FB / 2 = 6/2 = 3 cm.

The fourth point of the section, point P, is the midpoint of the BC side of the base of the pyramid.

Then KR is the middle line of the triangle ABC.

The segments MN and KP are parallel to the AC side as centerlines, and therefore parallel to each other.

Similarly, MK is parallel to NP.

Then the section MNPK is a parallelogram, and then NP = MK = 3 cm, KP = MN = 4 cm.

Rsech = 2 * (MK + KR) = 2 * (3 + 4) = 2 * 7 = 14 cm.

Answer: The perimeter of the section is 14 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.