Hi there!
The way to do this is to find the area of the circle and then subtract the area of the triangle.
Finding the area of the circle:
We know the formula for the area of a circle is just [tex]\pi r^2[/tex], where r is the radius. We know we are using 3.14 for pi, so it becomes [tex]3.14r^2[/tex]. Now, we just need the radius. We can see that there are two points on the circle given, (0,10) and (10,0). As both are 10 away from (0,0), and on the circle, we can reason that the radius is 10. Plugging this into the equation, we get:
[tex]3.14 (10^2)[/tex]
[tex]3.14(100)[/tex]
[tex]314\\[/tex]
Thus, we know the area of the circle is 314.
Finding the area of the triangle:
We know the formula for the area of a triangle is [tex]\frac{1}{2}bh[/tex]. We can see the base goes from (-6,-8) to (6,-8). Since the y coordinate is the same here, we know the distance is just in the x coordinates. The x coordinates are -6 and 6, and the distance between these is |6 - (-6)|, or 12. This gives us a base of 12.
Now, in terms of the height, we see that the y coordinate of the base is at -8 for both points, thus we can reason the point (0,-8) is on the line. This serves as our height, from (0,-8) to (0,10). The distance between these two points is |10 - (-8)|, or 18. This gives us a height of 18.
Substituting this all in, we get:
[tex]\frac{1}{2}(12)(18)[/tex]
[tex]6(18)[/tex]
[tex]108\\[/tex]
Thus, we know the area of the triangle is 108.
Putting it together:
Subtract the area of the triangle from the area of the circle. 314 - 108 = 206.
Hope this helps! Don't be afraid to ask questions if any of this doesn't make sense.
