Answer: [tex]A= 32(\pi-2)\ cm^2, \ \ \ P=8\pi\ cm[/tex]
Step-by-step explanation:
When we consider Area under arc AC is is representing a quarter as ADBC is a square, [tex]\angle D=90^{\circ}[/tex].
Area of quadrant = [tex]\dfrac{\pi r^2}{4}[/tex]
here r= 8 cm
Area under Arc AC= [tex]\dfrac{\pi (8)^2}{4}=16\pi\ cm^2[/tex]
Area of white region ABC = Area of square ADBC - Area under Arc AC
[tex]=8^2-16\pi\ \ [\text{Area of square} = sides^2]\\\\= 64-16\pi\ \ =16(4-\pi)\ cm^2[/tex]
Similarly , Area of white region ADC = [tex]16(4-\pi)\ cm^2[/tex]
Area of shaded region = Area of square - Area of white region ABC - Area of white region ADC
[tex]=64-(64-16\pi)-(64-16\pi)\\\\= 32\pi-64\ cm^2 \\\\= 32(\pi-2)\ cm^2[/tex]
Area of shaded region =[tex]= 32(\pi-2)\ cm^2[/tex]
Length of arc AC = [tex]\dfrac{Circumference}{4}=\dfrac{2\pi r}{4}[/tex]
[tex]\dfrac{\pi (8)}{2}=4\pi cm[/tex]
Perimeter of shaded region = 2(AC) = [tex]8\pi\ cm[/tex]
