ABCA1B1C1 is a regular triangular prism, the length of the base edge of which is 6 cm. Point M is the midpoint

| March 1, 2021 | education

ABCA1B1C1 is a regular triangular prism, the length of the base edge of which is 6 cm. Point M is the midpoint of the edge A1C1. Calculate the length of the orthogonal projection of the line segment MB on the plane ABC.

Since, according to the condition, the prism is correct, then an equilateral triangle lies at its base, and the side faces are rectangles.

Point M is the middle of A1C1, we lower the perpendicular MH from it to the edge AC of the base, then point H also divide AC in half, AH = CH = AC / 2 = 6/2 = 3 cm.

The ВН segment is our desired projection of the BM segment on the ABC plane.

By the Pythagorean theorem, from the triangle ABН, BH ^ 2 = AB ^ 2 – AH ^ 2 = 6 ^ 2 – 3 ^ 2 = 36 – 9 = 27.

BH = √27 = 3 * √3 cm.

Answer: The length of the projection   is 3 * √3 cm.



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