+0  
 
0
35
1
avatar

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?

 

 May 5, 2020
 #1
avatar+1502 
+2

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!

 May 5, 2020

30 Online Users

avatar
avatar
avatar