SOLUTION: I dont understand how to do this I have to find the area of the larger segment whose chord is 8 inches long in a circle with an 8 inch radius. I am not following any of how to do

Algebra ->  Circles -> SOLUTION: I dont understand how to do this I have to find the area of the larger segment whose chord is 8 inches long in a circle with an 8 inch radius. I am not following any of how to do       Log On


   

Question 1166909: I dont understand how to do this I have to find the area of the larger segment whose chord is 8 inches long in a circle with an 8 inch radius. I am not following any of how to do these problems I am very confused
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

The area of the smaller segment is exactly  1%2F6  of the area of the circle.


Hence, the area of the larger segment is  5%2F6  of the circle area.




Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The chord is 8 inches long, and the radius of the circle is 8 inches. So the triangle formed by the chord and the two radii to the endpoints of the chord form an equilateral triangle.

Each angle of an equilateral triangle is 60 degrees, which is 1/6 of a full circle of 360 degrees.

So the area of the smaller segment of the circle is 1/6 the area of the whole circle; therefore, the area of the larger segment is 5/6 the area of the whole circle.

Use the given radius in the formula for the area of a circle and multiply the result by 5/6.