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(A) $1$. The diagonal of the rectangle $ABCD$ is the diameter of the circle.$2$. Using the Pythagorean theorem in $	riangle ABC$,the diagonal $AC = \

Vedclass · Accepted Answer

$30.5$

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(A) $1$. The diagonal of the rectangle $ABCD$ is the diameter of the circle.$2$. Using the Pythagorean theorem in $	riangle ABC$,the diagonal $AC = \sqrt{AB^2 + BC^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, cm$.$3$. The diameter of the circle is $10 \, cm$,so the radius $r = 5 \, cm$.$4$. The area of the circle is $\pi r^2 = 3.14 	imes 5^2 = 3.14 	imes 25 = 78.5 \, cm^2$.$5$. The area of the rectangle $ABCD$ is $AB 	imes BC = 8 	imes 6 = 48 \, cm^2$.$6$. The area of the shaded region is the area of the circle minus the area of the rectangle: $78.5 - 48 = 30.5 \, cm^2$.

As shown in the diagram,rectangle $ABCD$ is inscribed in a circle. If $AB = 8 \, cm$ and $BC = 6 \, cm$,find the area of the shaded region in the diagram. $(\pi = 3.14)$ (in $cm^2$)

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