Question

Find area of unshaded region.

Answer 1

Area of unshaded region = Area of Chord (1) + Area of smaller sector(2) + Area of unshaded region (3)

Area of chord (1) =Area of sector - Area of shaded triangle

Area of sector = (108/360)*π*12*12 = 43.2π 

Area of shaded triangle:

Angle between sides of triangle:  180 - 72 = 108 degrees.

Area of triangle = 0.5 * 12 *12*sin108°= 72sin108°

Area of chord (1) =Area of sector - Area of shaded triangle
    
                             = 43.2π - 72sin108°

 Area of smaller sector(2)

Area of sector smaller (2)  = (72/360)*π*12*12 = 28.8π 

Area of region (3)

Area of unshaded region (3) = Area of large triangle - Area of smaller sector - Area of shaded triangle.

Area of large triangle = 0.5*24*19*sin36°= 228sin36°

 
Area of unshaded region (3) = Area of large triangle - Area of smaller sector - Area of shaded triangle.
   
                               =  228sin36° - 28.8π  - 72sin108°

Total unshaded area :

=  (43.2π - 72sin108°) + (28.8π) + (228sin36° - 28.8π  - 72sin108°)

=  43.2π - 72sin108° + 228sin36° - 72sin108°

= 43.2π + 228sin36° - 144sin108°

≈ 132.78 cm²

Answer 2

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