Exercise 44 Page 569

To evaluate the area of the shaded region, we should subtract the area of a triangle from the area of a circle. Let's start with evaluating the area of a circle. Recall the formula for the area of a circle with a radius of r. π r^2 Now, let's recall the formula for the area of a triangle. In this formula a is the base and h is the height of this triangle. 1/2ah As we can see, the height of the drawn triangle is r and the base is 2r. Let's substitute these values in the above formula.

1/2ah

SubstituteII

a= 2r, h= r

1/2( 2r)( r)

FracMultDenomToNumber

a/2* 2 = a

1(r)(r)

Multiply

Multiply

r^2

The area of the triangle is r^2. Finally, let's subtract this area from the area of the whole circle. π r^2-r^2 This corresponds with answer J.