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In the given figure, $OABC$ is a quadrant of a circle with centre $O$ and radius $8\text{ cm}$. If $OD = 6\text{ cm}$, then find then perimeter of the shaded region.
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Perimeter of the shaded region $= \text{length of Arc } ABC + AD + CD$
$= \frac{90}{360} \times 2 \times \frac{22}{7} \times 8 + \sqrt{6^2 + 8^2} + (8 - 6)$ [$1\frac{1}{2}$ marks]
$= \frac{172}{7}\text{ cm or } 24.57\text{ cm}$ [$\frac{1}{2}$ mark]
$= \frac{90}{360} \times 2 \times \frac{22}{7} \times 8 + \sqrt{6^2 + 8^2} + (8 - 6)$ [$1\frac{1}{2}$ marks]
$= \frac{172}{7}\text{ cm or } 24.57\text{ cm}$ [$\frac{1}{2}$ mark]