SOLUTION: how do you find the perimeter of a shaded region of a circle the shaded region is 140 degrees the area of the shaded region is 126π

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Question 979530: how do you find the perimeter of a shaded region of a circle
the shaded region is 140 degrees
the area of the shaded region is 126π
Found 4 solutions by josgarithmetic, Edwin McCravy, josmiceli, AnlytcPhil:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Two radii and the length of the arc with this radius.


The fraction of the full-circle's area given to be equal to .






The length of the arc, .

The perimeter of this sector is .
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
If you can find the radius, then
the problem is solved, since
Circumference =
--------------------------
The whole circle is degrees of arc

Let = the area of the whole circle
I can say:



I know that:
,so



and



-----------------
The perimeter of the shaded rgion is:

answer
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!

The whole figure is a sector of a circle. The area of a sector of a circle
is given by the formula:

 where q is in radians.

We convert q = 140° to radians:







Multiply both sides by 18



Divide both sides by 7p







The length of the arc is found by the formula

 where q is in radians.





The perimeter is made up of two radii and the arc at the top:

Perimeter = 

Edwin
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