Question

Find the area of the sector whose length of the arc is 58 cm. and

the radius is 10 cm.​

Answer 1

AnswEr :

• Area of the sector = 290 cm²

Explanation :

We're given with the radius as well as length of the sector, that is,

• Length of the sector = 58 cm.

• Radius of the sector = 10 cm.

Now,

As we're given with length of the sector and radius of the sector we know the required formula, that is,

$: \implies \sf \: \: Area = \dfrac{r}{2} \times Length \: of \: arc$

Substituting the values,

$: \implies \sf \: \: Area = \dfrac{10}{2} \times 58 \\ \\ \\ : \implies \sf \: \: Area = 10 \times 29 \\ \\ \\ : \implies \sf \: \: { \boxed{ \frak{ \purple{Area = 290 \: {cm}^{2} }}}} \: \bigstar$

Therefore, area of the sector is 290 cm².

Additional information :

• Area of Sector = θ × π 360 × r²

• Area of Segment = ( θ × π 360 − sin(θ)2 ) × r²

• L = θ × π180 × r

In above formula's the value of θ is in degrees.

Answer 2

Given ,

• Length of arc = 58 cm
• Radius of circle = 10 cm

We know that , the area of sector is given by

$\boxed{ \tt{Area \: of \: sector = \frac{radius}{2} \times length \: of \: arc}}$

Thus ,

Area = 10/2 × 58

Area = 5 × 58

Area = 290 cm²

Therefore , the area of sector is 290 cm²

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