The radius of the circle is \large 1 m. What is the area of the shaded region

Correct Answer

As suggested by the animation, the leaf shape is really a distorted circle and has exactly the same area of the circle.

Notice that the base of the rectangle is half the circumference of the circle and the height is two time the radius.

Also, recall that the diagonal bisects the rectangle. Thus, the area of the rectangle equals to the area of the leaf shape plus two times the shaded area.

\large A_{rectangle}=2A_{shaded}+A_{leaf}

\large A_{shaded} =frac{1}{2}(A_{rectangle} - A_{leaf})

                   \large =\frac{1}{2}(bh- A_{circle})

                   \large =\frac{1}{2}\left( \left(\frac{1}{2}(2 \pi r)\right)(2r)-\pi r^2\right)

                  \large =\frac{1}{2}(2\pi r^2-\pi r^2) 

                  \large =\frac{\pi r^2}{2}

                \large =\frac{\pi}{2} m^2