ABCD is a square with sides 8 cm long. Two circles each with radius 8 cm are drawn, one with center A and the other with center C. Find the area of the region inside both circles.

geduiwelh 2021-08-01 Answered
ABCD is a square with sides 8 cm long. Two circles each with radius 8 cm are drawn, one with center A and the other with center C.
Find the area of the region inside both circles.

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Expert Answer

izboknil3
Answered 2021-08-02 Author has 15890 answers
Step 1
Area of square.
\(\displaystyle{A}={\left({s}\right)}^{{{2}}}={\left({8}\right)}^{{{2}}}={64}{c}{m}^{{{2}}}\)
now area of circle inside the circles
\(\displaystyle{A}=\pi{r}^{{{2}}}\)
\(\displaystyle{A}={32}\pi\)
Now
Area of region inside both the \(\displaystyle\circ\le{s}={a}{r}{e}{a}\) of two quarter circles - area of square.
i.e.
\(\displaystyle{A}={32}\pi-{64}\)
\(\displaystyle{A}={32}\pi-{64}{c}{m}^{{{2}}}\)
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