First, let's calculate the area of the rectangle. Find the distances between the length and the width. For the width we can use point A and point D.
(2, 2) and (20, 2)
20 - 2 = 18
So the width is 18 cm. Now find the length. We can use point A and point B.
(2, 2) and 2, 26)
26 - 2 = 24
So the length is 24.
[tex]\sf A=lw[/tex]
[tex]\sf A=(24)(18)[/tex]
[tex]\sf A=432cm^2[/tex]
So the area of the rectangle is 432 square centimeters, now let's find the area of the circle.
The radius is given as 15 cm. Use 3.14 to approximate for pi.
[tex]\sf A=\pi r^2[/tex]
[tex]\sf A\approx (3.14)(15)^2[/tex]
[tex]\sf A\approx (3.14)(225)[/tex]
[tex]\sf A\approx 706.5cm^2[/tex]
So the area of the circle is approximately 706.5 square centimeters. Subtract this area from the area of the rectangle to find the value of the shaded area.
[tex]\sf 706.5-432=\boxed{\sf 274.5cm^2}[/tex]
