Two sectors of a circle are inscribed in an isosceles right triangle with length of the legs of 10. What is the area of the red region?
Since it's isoceles right, the angles must be 45-45-90.
That means that the hypothenuse is sqrt(200).
We just need to find the length of half the hypothenuse, since the unshaded is 45/360 of a circle.
sqrt(200)= sqrt(4*50) = 2(sqrt(50)).
The radius is (2(sqrt(50)))/2 = sqrt(50).
area of circle is π r^2, so it's 50π. The part is 45/360 of a circle, with two parts, so 90/360 = 45/180 = 1/4
50π/4 is the unshaded.
The triangle has an area of 10*10/2 = 50.
50 - 50π/4 is the area of the red.
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