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