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Mkey [24]
3 years ago
13

I need help with my rsm hwrk pls help me

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
3 0

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

Step-by-step 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 = \dfrac{\pi r^2}{4}

here r= 8 cm

Area under Arc AC= \dfrac{\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 = \dfrac{Circumference}{4}=\dfrac{2\pi r}{4}

\dfrac{\pi (8)}{2}=4\pi cm

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

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