Question

Find the perimeter of the given figure , where O is the centre of the given sector ​

Answer 1

AnSwer:-

• The perimeter of the given figure is 282 cm.

GiVen:-

• Here, radius of the circle is 42 cm

ExPlanation :-

${\bigstar{ \underline{ \sf{Circumference \: of \: the \: Circle : }}}}\\ \sf \: =2\pi \: r \\ \sf \: = 2 \times \dfrac{22}{7} \times 42 \\ \sf = 264cm$

${\boxed{\boxed{ \tiny{\sf {\: Perimeter = \: circumference \: of \: the \: circle - length \: + 2(radius)}}}}}$

$\sf \: For \: arc \: AB , Central \: angle = {90}^{ \circ}$

$\sf \: Length \: of \: arc = \dfrac{x}{360} \times circumference \\ \sf \: here \: x \: is \: central \: angle.$

${\bigstar{ \underline{\sf {\: Length \: of \: arc \: AB = }}}}\\ \sf \implies \dfrac{90}{360} \times 264 \\ \sf \implies66cm$

Now ,

${\bigstar{\underline{\sf {\: Perimeter \: of \: the \: circle =}}}} \\ \sf \longmapsto \: 264 - 66 + 2(42) \\ \sf \longmapsto \: 198 + 84 \\ \sf \longmapsto \:282cm$

Hence, the perimeter is 282 cm.