Question

I need help with my rsm hwrk pls help me

Answer 1

Answer:
`A= 32(\pi-2)\ cm^2, \ \ \ P=8\pi\ cm`

Explanation:

When we consider Area under arc AC is is representing a quarter as ADBC is a square,
`\angle D=90^(\circ)`.

Area of quadrant =
`(\pi r^2)/(4)`

here r= 8 cm

Area under Arc AC=
`(\pi (8)^2)/(4)=16\pi\ cm^2`

Area of white region ABC = Area of square ADBC - Area under Arc AC

`=8^2-16\pi\ \ [\text{Area of square} = sides^2]\\\\= 64-16\pi\ \ =16(4-\pi)\ cm^2`

Similarly , Area of white region ADC =
`16(4-\pi)\ cm^2`

Area of shaded region = Area of square - Area of white region ABC - Area of white region ADC

`=64-(64-16\pi)-(64-16\pi)\\\\= 32\pi-64\ cm^2 \\\\= 32(\pi-2)\ cm^2`

Area of shaded region =
`= 32(\pi-2)\ cm^2`

Length of arc AC =
`(Circumference)/(4)=(2\pi r)/(4)`

`(\pi (8))/(2)=4\pi cm`

Perimeter of shaded region = 2(AC) =
`8\pi\ cm`