Answer:
Area of Shaded Region [tex]=50\pi$ cm^2[/tex]
Area of Semicircle [tex]=50\pi$ cm^2[/tex]
[tex]\dfrac{\text{Area of Shaded region}}{\text{Area of Square}}=\dfrac{ \pi}{8}[/tex]
Step-by-step explanation:
Area of Shaded Region = Area of Sector - Area of Semicircle
Area of Sector
Radius of the sector =20cm
[tex]=\frac{90}{360}X\pi *20^2\\ =100\pi cm^2[/tex]
Area of Semicircle
Since AB is the diameter of the semicircle
Radius of the Semicircle=20/2=10cm
Area of semicircle
[tex]=\frac{\pi r^2}{2}\\ =\frac{\pi *10^2}{2}\\=50\pi cm^2[/tex]
Therefore, area of Shaded Region
[tex]=100\pi -50 \pi\\=50\pi$ cm^2[/tex]
Area of Square =20 X 20 [tex]=400 cm^2[/tex]
[tex]\dfrac{\text{Area of Shaded region}}{\text{Area of Square}} \\=\dfrac{50 \pi}{400} \\=\dfrac{ \pi}{8}[/tex]
