A perpendicular DM = 10 cm is drawn to the plane of the square ABCD. The side of the square is 6 cm

| November 16, 2020 | education

A perpendicular DM = 10 cm is drawn to the plane of the square ABCD. The side of the square is 6 cm. Calculate the lengths of the oblique MA, MC, MB and their projection lengths

First, let’s figure out what projections we will have.
The oblique AM projection is AD.
The oblique CM projection is CD.
The oblique BM projection is BD.
AD, CD are the sides of the squares, therefore they are equal to 6 cm.
BD is the diagonal of the square – we find by the Pythagorean theorem:
√ (AD ^ 2 + AB ^ 2) =√ (6 ^ 2 + 6 ^ 2) = 6 * √ (2) “)
And that we get:
AD = CD = 6cm
BD = 6 (2) cm
Now let’s find MA, MC, MB:
We find each of them by the Pythagorean theorem:
MA = √ (MD ^ 2 + AD ^ 2) = √ (100 + 36) = 2 (34) cm
MB = √ (MD ^ 2 + BD ^ 2) = √ (100 + 36) = 2 (34) cm
MC = √ (MD ^ 2 + CD ^ 2) = √ (100 + 72) = 2 (43) cm
Answer: AD = CD = 6 cm, BD = 6 (2) cm, MA = MB = 2 (34) cm, MS = 2 (43) cm.



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