There is a rectangle abcd, with sides ab = cd = 32, and sides and bc = da = 24. the rectangle is rotated 90° clockwise about c, then rotated 90° clockwise about the new location of point that d after the first rotation. what is the length of the path travelled by point a?

Answer

given,

side of rectangle, AB = CD = 32

                              BC = DA = 24

rectangle is rotated 90° clockwise about C.

then rotated 90° clockwise about D.

Path traveled by the point A for first rotation will be in circle with radius AC.

             AC = 40

             θ₁ = 90°

         D₁ = 1256.64

For the second rotation Point A will move in circular path with radius of AD

             AD = 24

             θ₁ = 90°

         D₂ = 452.39

total path traveled by the point A

   D = D₁ + D₂

   D = 1256.64 + 452.39

  D = 1709.03

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step-by-step explanation:

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