Quarter Circle

Geometry Level 1

In the above quarter circle of radius 1, what is the area of the blue region?

π 8 \frac{ \pi } { 8 } π − 3 4 \frac{ \pi - 3 } { 4 } π − 2 4 \frac{ \pi - 2 } { 4 } π − 1 6 \frac{ \pi - 1 } { 6 }

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Chung Kevin by Chung Kevin , 45, Australia

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1 solution

Krishna Shankar
Apr 23, 2015

Area of the triangle comes out to be 1/2

and area of a segment of circle is 1/4 pi r^2 & r=1

By subtracting area of segment & triangle

the answer comes out to be pi-2/4

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Good. If it's not a quarter circle (that is the angle of arc formed is not π 2 \frac {\pi}{2} ), but some angle 0 < θ < π 0 < \theta < \pi . Can you find a general equation such that the ratio between the blue region and the red region is m : 1 m : 1 ?

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