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taurus [48]
3 years ago
9

Find area of unshaded region.

Mathematics
2 answers:
Paraphin [41]3 years ago
8 0

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°

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

 Area of smaller sector(2)

Area of sector smaller (2)  = (72/360)*π*12*12 = 28.8π<span> 
</span>
<span>Area of region (3)
</span>
<span>Area of unshaded region (3) = Area of large triangle - Area of smaller sector - Area of shaded triangle.
</span>
Area of large triangle = 0.5*24*19*sin36°= 228sin36°

 
<span>Area of unshaded region (3) = Area of large triangle - Area of smaller sector - Area of shaded triangle.
</span>   
                               =  228sin36° - 28.8π  - <span>72sin108°
</span>
Total unshaded area :

=  (43.2π - 72sin108°) + (28.8π) + (228sin36° - 28.8π  - <span>72sin108°)
</span>
=  43.2π - 72sin108° + 228sin36° - <span>72sin108°
</span>
= 43.2π <span>+ </span><span>228sin36° - 144sin108</span>°

≈ 132.78 cm²
Kipish [7]3 years ago
3 0
If you have any question, ask please :D

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