SOLUTION: Find the area of the shaded region. https://imgur.com/a/IaHCHvI

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Question 1205049: Find the area of the shaded region.
https://imgur.com/a/IaHCHvI
Found 2 solutions by mananth, Edwin McCravy:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
1. Area of sector - area of triangle = area of shaded portion
CM = 16* sin 27.5 degrees =7.3879*2=14.775
OM = 16* cos 27.5 degrees =14.19
Area of triangle = 1/2 *14.775*14.19=104.828 cm^2
Area of sector = %28%28theta%29%2F360%29%2Api%2Ar%5E2


= %28%2855%29%2F360%29%2Api%2A16%5E2=122.87 cm^2


122.87-104.828= 18.042 cm^2 approx Area of shaded portion.


OR you can directly use the formula given below


A = %281%2F2%29+%2Ar%5E2%2A+%28%28pi%2A%28theta%29%2F180%29+-sin+%28theta%29%29


A=5*256*((pi*55/180)-sin55degrees)


.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Area of the segment marked with X:



The area of the whole sector is  



The area of the triangle is

A=%28a%29%28b%29sin%28theta%29+=+16%2A16%2Asin%2855%5Eo%29=104.8514617

Answer = area of sector - area of triangle = 122.8711793-104.8514617 =

18.0197176 cm2

Edwin