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If the perimeter of a sector of a circle of radius 5.6 cm is 17.2 cm, find the area of the sector

Posted by Amit Gupta 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let OAB be the given sector
Let arc AB = {tex}l{/tex}
Perimeter of sector OAB = 27.2m
{tex} \Rightarrow {/tex} OA + OB + ARC AB = 27.2
{tex} \Rightarrow {/tex} {tex}l{/tex} = 27.2 - (5.7 + 5.7) = 15.8M
Now, length of arc {tex} = \frac{\theta }{{360}} \times 2\pi r{/tex}
{tex}\frac{{15.8}}{{2\pi r}} = \frac{\theta }{{360}}{/tex}
Area of sector AOB {tex} = \frac{\theta }{{360}} \times \pi {r^2}{/tex}
{tex} = \frac{{5.8}}{{2\pi r}} \times \pi {r^2}{/tex}
= 7.9r
{tex} = 7.9 \times 5.7{/tex}
= 45.03m²

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