$¯ ¯¯¯¯¯¯ ¯ O A$ and $¯ ¯¯¯¯¯¯ ¯ O B$ are perpendicular radii of a circle. If perimeter of minor sector is 20 cm, then find area of the minor segment.

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Solution

Area of minor segment $= π r^{2} \times \frac{90}{360}$
Perimeter $= 2 r + (2 π r \times \frac{90}{360}) = 20$
$\Rightarrow 2 r (1 + \frac{π}{4}) = 20$
$\Rightarrow r = \frac{10}{1 + \frac{π}{4}}$
$\Rightarrow$ Area $= \frac{π r^{2}}{4} = \frac{π}{4} (\frac{100}{(4 + π)^{2}}) 16 = \frac{400 π}{(π + 4)^{2}}$ .

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¯¯¯¯¯¯¯¯OA and ¯¯¯¯¯¯¯¯OB are perpendicular radii of a circle. If perimeter of minor sector is 20 cm, then find area of the minor segment.

Area of minor segment=πr2×90360Perimeter=2r+(2πr×90360)=20⇒2r(1+π4)=20⇒r=101+π4⇒ Area =πr24=π4(100(4+π)2)16=400π(π+4)2.

$¯ ¯¯¯¯¯¯ ¯ O A$ and $¯ ¯¯¯¯¯¯ ¯ O B$ are perpendicular radii of a circle. If perimeter of minor sector is 20 cm, then find area of the minor segment.