The length of the edge of the cube ABCDA1B1C1D1 is 4 cm. Calculate the distance between line AD and plane CD1A1.

univerkov | August 1, 2021 | education

Since the figure is a cube, then the ABCD face is perpendicular to the DD1C1C face, then the DC1 diagonal is perpendicular to the AD edge.

The side faces of the cube are squares, then the diagonals DC1 and CD1 are equal, intersect at right angles and are divided in half.

Then the segment DH is perpendicular to the diagonal CD and the plane CD1A1.

By the Pythagorean theorem, we determine the length of the diagonal DC1.

DC1 ^ 2 = CD ^ 2 + CC1 ^ 2 = 16 + 16 = 32.

DC1 = 4 * √2 cm.

Then DH = DC1 / 2 = 2 * √2 cm.

Answer: From the straight line АD of the plane СD1А1 2 * √2 cm.

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