In the figure,AB is a diameter of the circle, | vedclass

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(C) Given,$AC = 6 \, cm$ and $BC = 8 \, cm$.We know that an angle in a semi-circle is a right angle. Therefore,$\angle C = 90^{\circ}$.In the right-an

Vedclass · Accepted Answer

$54.5$

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(C) Given,$AC = 6 \, cm$ and $BC = 8 \, cm$.We know that an angle in a semi-circle is a right angle. Therefore,$\angle C = 90^{\circ}$.In the right-angled $	riangle ACB$,using the Pythagoras theorem:$AB^2 = AC^2 + BC^2$$AB^2 = 6^2 + 8^2 = 36 + 64 = 100$$AB = \sqrt{100} = 10 \, cm$ (since length cannot be negative).Area of $	riangle ACB = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 8 	imes 6 = 24 \, cm^2$.The diameter of the circle is $AB = 10 \, cm$,so the radius $r = \frac{10}{2} = 5 \, cm$.Area of the circle $= \pi r^2 = 3.14 	imes (5)^2 = 3.14 	imes 25 = 78.5 \, cm^2$.Area of the shaded region = Area of the circle - Area of $	riangle ACB$$= 78.5 - 24 = 54.5 \, cm^2$.

In the figure,$AB$ is a diameter of the circle,$AC = 6 \, cm$ and $BC = 8 \, cm$. Find the area of the shaded region (Use $\pi = 3.14$). (in $cm^2$)

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