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Three of the four vertices of a rectangle are $(5, 11)$, $(16, 11)$ and $(16, -2)$. What is the area of the intersection of this rectangular region and the region inside the graph of the equation $(x - 5)^2 + (y + 2)^2 = 9$? Express your answer as a common fraction in terms of pi.

 Jan 15, 2018
 #1
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The other vertex  of the rectangle is  the circle's center  =   (5, -2)

 

Look  at the image here :  

 

 

The region common to both areas is just  the quarter circle  area  of the given circle

 

And this circle has a radius  of 3.....so....the quarter circle has an area  of

 

pi (r^2)  / 4  =   pi (3^2)  / 4  =    (9/4)pi   units ^2

 

 

cool cool cool

 Jan 15, 2018

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