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.
[tex]D_1 = \dfrac{\theta_1}{360^0}\times \pi \times {AC}^2[/tex]
[tex]AC = \sqrt{24^2+32^2}[/tex]
AC = 40
θ₁ = 90°
[tex]D_1 = \dfrac{90^0}{360^0}\times \pi \times {40}^2[/tex]
D₁ = 1256.64
For the second rotation Point A will move in circular path with radius of AD
[tex]D_2 = \dfrac{\theta_2}{360^0}\pi {AD}^2[/tex]
AD = 24
θ₁ = 90°
[tex]D_2 = \dfrac{90^0}{360^0}\times \pi \times {24}^2[/tex]
D₂ = 452.39
total path traveled by the point A
D = D₁ + D₂
D = 1256.64 + 452.39
D = 1709.03
