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.

Guest Jan 15, 2018

#1**+2 **

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

CPhill
Jan 15, 2018