DABC-tetrahedron, points M and F-midpoints of edges AD and DC, respectively.

| January 26, 2021 | education

DABC-tetrahedron, points M and F-midpoints of edges AD and DC, respectively. Construct a section of the tetrahedron with the MBF plane and calculate its perimeter if the edge length of the tetrahedron is 4 cm.

The base and side faces of the tetrahedron are equilateral triangles with sides of 4 cm.

Since points M and F are the middle of the lateral edges, the segment MF is the midline of the AСD triangle, and the segments BM and BF are the heights and medians of the lateral faces.

Then MF = AC / 2 = 4/2 = 2 cm, BM = AM = CF = DF = 4/2 = 2 cm.

In a right-angled triangle ABM, according to the Pythagorean theorem, BM^2 = AB^2 – AM^2 = 16 – 4 = 12.

ВМ = ВF = 2 * √3 cm.

The section perimeter will be equal to: Рвмf = 2 * ВМ + MF = 2 * 2 * √3 + 2 = 2 * (2 * √3 + 1) cm.

Answer: The perimeter of the section is 2 * (2 * √3 + 1) cm.



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