Question

Find the area of sector when perimeter of sector with radius 14cm is 68cm

Answer 1

[ Figure in the attachment ]

Given :- Radius ( r ) of circle = 14 cm

perimeter of sector = 68 cm

Solution :-

$perimeter \: of \: sector = lenght \: of \: sector \: + 2r$

$68 = \frac{ \alpha }{360} 2\pi \: r \: + 2r$

$68 = 2 \times 14( \frac{ \alpha }{360} \times \frac{22}{7} + 1)$


$\frac{17}{7} = \frac{11 \alpha + 1260}{1260}$

$17 = \frac{11 \alpha + 1260}{180}$

$3060 = 11 \alpha + 1260$

$1800 = 11 \alpha$


$\frac{1800}{11} = \alpha$

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• area of sector =
$\frac{ \alpha }{360} \times \pi \: {r}^{2}$
$= \frac{ \frac{1800}{11} }{360} \times \frac{22}{7} \times 14$

$= \frac{1800}{11} \times \frac{1}{360} \times \frac{22}{7} \times 14$

$= 20 \: {cm}^{2}$

Answer 2

Answer:

Area of sector is 476 square centimeter.

Step-by-step explanation:

Given the perimeter of sector with radius 14cm is 68cm.

we have to find the area of sector.

$\text{Length of arc=}\frac{\theta}{360^{\circ}}\times2\pi r$

⇒ $\frac{L}{2\pi r}=\frac{\theta}{360^{\circ}}$    →     (1)

$\text{Area of sector =}\frac{\theta}{360^{\circ}}\times \pi r^2$

Using equation (1)

$\text{Area = }\frac{L}{2\pi r}\times \pi r^2\\\\=\frac{L}{2}\times r = \frac{68}{2}\times14=476cm^2$

Hence, area of sector is 476 square centimeter.