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?
+1005 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.
If you don't understand anything feel free to ask!
