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.
![D_1 = \dfrac{\theta_1}{360^0}\times \pi \times {AC}^2](https://tex.z-dn.net/?f=D_1%20%3D%20%5Cdfrac%7B%5Ctheta_1%7D%7B360%5E0%7D%5Ctimes%20%5Cpi%20%5Ctimes%20%7BAC%7D%5E2)
![AC = \sqrt{24^2+32^2}](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B24%5E2%2B32%5E2%7D)
AC = 40
θ₁ = 90°
![D_1 = \dfrac{90^0}{360^0}\times \pi \times {40}^2](https://tex.z-dn.net/?f=D_1%20%3D%20%5Cdfrac%7B90%5E0%7D%7B360%5E0%7D%5Ctimes%20%5Cpi%20%5Ctimes%20%7B40%7D%5E2)
D₁ = 1256.64
For the second rotation Point A will move in circular path with radius of AD
![D_2 = \dfrac{\theta_2}{360^0}\pi {AD}^2](https://tex.z-dn.net/?f=D_2%20%3D%20%5Cdfrac%7B%5Ctheta_2%7D%7B360%5E0%7D%5Cpi%20%7BAD%7D%5E2)
AD = 24
θ₁ = 90°
![D_2 = \dfrac{90^0}{360^0}\times \pi \times {24}^2](https://tex.z-dn.net/?f=D_2%20%3D%20%5Cdfrac%7B90%5E0%7D%7B360%5E0%7D%5Ctimes%20%5Cpi%20%5Ctimes%20%7B24%7D%5E2)
D₂ = 452.39
total path traveled by the point A
D = D₁ + D₂
D = 1256.64 + 452.39
D = 1709.03
Answer:
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