SOLUTION: Find the area of the shaded segment of circle O to the nearest tenth of a square unit. The radius of the circle is 6 units. The perpendicular from O to the chord joining point A to

Algebra ->  Circles -> SOLUTION: Find the area of the shaded segment of circle O to the nearest tenth of a square unit. The radius of the circle is 6 units. The perpendicular from O to the chord joining point A to      Log On


   

Question 1163056: Find the area of the shaded segment of circle O to the nearest tenth of a square unit. The radius of the circle is 6 units. The perpendicular from O to the chord joining point A to point B measures 4 units. This Is the link to the diagram. https://drive.google.com/file/d/1-nFHdeNhm8pyfkVN1HXpfg6ckeoBaM7b/view?usp=drivesdk
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Find the area of the shaded segment of circle O to the nearest tenth of a square unit. The radius of the circle is 6 units.
The perpendicular from O to the chord joining point A to point B measures 4 units.
:
Find the area of the circle:
A = pi%2A6%5E2
A = 113.1 sq/units
:
Find the arc angle using the cosine of the two right triangles
cos(C) = 4%2F6
C = 48.2 degrees
The arc angle: 2 * 48.2 = 96.4 degrees
:
Find area of the given arc
96.4%2F360 * 113.1 = 30.3 sq/units
:
Find the area of the two right triangles
find the base (b) of the triangle using the sine of 48.2
sin(48.2) = b%2F6
b = sin(48.2) * 6
b = 4.47 units
Find the area
A = .5*4.47*4
A = 8.9 sq/units
2 * 8.9 = 17.9 sq/units the area of the 2 right triangles
:
Find f
subtract area of the two right triangle from the arc area
30.3 - 17.9 = 12.4 sq/units the area of f