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# Area of a shaded region

CCSS.Math:

## Video transcript

we're asked to find the area of the shaded region so the area of this red shaded region so this is interesting this is almost a 10 by 10 square except we have these quarter circles that are cut out so the area of this would be the area of what a 10 by 10 square would be minus the area of these quarter circles and each of these quarter circles it's a quarter of a circle with a radius 3 I think we can assume that all of these if you took the distance from here to the outside of this quarter circle and have radius 3 so if you put four quarter circles together you're going to have a complete white circle so one way to think about this is that the area of this whole red region is going to be the area of the entire square which is 10 by 10 so it's going to be 10 times 10 which is 100 whatever square units we have and then we're going to subtract out the we're going to subtract out the area of the four quarter circles and that area is going to be equivalent to one Cirque the area of one circle with a radius of three so what's the area of a circle with radius three well the formula for area of a circle is PI R squared or R squared pi so the radius is three so it's going to be 3 times 3 which is 9 times pi 9 pi so we have a hundred minus nine pi is the area of the shaded region and we got it right