Question

Find the area of the shaded region.

Answer 1

27π

Explanation:

Imagine that this circle was complete. As you can see, only 3 / 4th of the circle remains, with respect to this whole circle. This is not an assumption, though it does appear so. The portion missing forms a right angle with the radii, and thus by definition, that portion is a quarter of a circle.

________

The simplest approach is to assume this circle to be complete, and solve for that area - provided the radii being 6 inches. Afterward we can take 3 / 4th of this area, solving for the area of the shaded region. After all, this circle is 3 / 4ths of our " complete circle. "

Area of an Imaginary " Complete Circle " = π
`r^2` = π
`(6)^2` = 36π,

Area of Shaded Region ( 3 / 4th of the " Complete Circle " ) =
`(3)/(4)`( 36π ) = 27π

27π is the exact area of the shaded region. If you want an approximated area, take π as 3.14, or a similar quantity to that.

Answer 2

The answer would be 27π

Explanation:

the area is 36pi and the shaded region is 3/4 of the circle, as a 90 degree angle is 1/4 of a 360 degree circle. 3/4 of 36pi is 27pi