Question

please answer it fast I will mark you branliest​

Answer 1

Given

• Radius of circle = 7 cm
• There are 3 sectors making an angle of 80°,60° & 40°

To Find

• The area of the shaded region?

Solition

$\displaystyle\star\underline{\boxed{\sf Area \ of \ sector = \dfrac{\theta}{360} \pi r^2}}$

✭ Area of sector making an angle of 40°

➝ $\displaystyle\sf Area \ of \ sector = \dfrac{\theta}{360} \pi r^2$

➝ $\displaystyle\sf Area = \dfrac{40}{360} \times \dfrac{22}{7} \times 7^2$

➝ $\displaystyle\sf Area = \dfrac{1}{9} \times \dfrac{22}{7} \times 14$

➝ $\displaystyle\sf Area = \dfrac{1}{9} \times 22\times 7$

➝ $\displaystyle\sf Area = \dfrac{1}{9} \times 154$

➝ $\displaystyle\sf \red{Area = 17.1 \ m^2}$

✭ Area of sector making an angle of 60°

➝ $\displaystyle\sf Area \ of \ sector = \dfrac{\theta}{360} \pi r^2$

➝ $\displaystyle\sf Area = \dfrac{60}{360} \times \dfrac{22}{7} \times 7^2$

➝ $\displaystyle\sf Area = \dfrac{1}{6} \times \dfrac{22}{7} \times 14$

➝ $\displaystyle\sf Area = \dfrac{1}{6} \times 22\times 7$

➝ $\displaystyle\sf Area = \dfrac{1}{6} \times 154$

➝ $\displaystyle\sf \purple{Area = 25.7 \ m^2}$

✭ Area of sector making an angle of 80°

➝ $\displaystyle\sf Area \ of \ sector = \dfrac{\theta}{360} \pi r^2$

➝ $\displaystyle\sf Area = \dfrac{80}{360} \times \dfrac{22}{7} \times 7^2$

➝ $\displaystyle\sf Area = \dfrac{2}{9} \times \dfrac{22}{7} \times 14$

➝ $\displaystyle\sf Area = \dfrac{2}{9} \times 22\times 7$

➝ $\displaystyle\sf Area = \dfrac{2}{9} \times 154$

➝ $\displaystyle\sf \orange{Area = 34.2 \ m^2}$

✭ Area of the shaded region

➝ $\displaystyle\sf ar(sector 1) + ar(sector 2) + ar(sector 3)$

➝ $\displaystyle\sf 17.1 + 25.7 + 34.2$

➝ $\displaystyle\sf \pink{Area = 77 \ m^2}$

Answer 2

Answer:

Area of shaded region is 60.969004 $cm^{2}$

Step-by-step explanation:

The formula for the area of the shaded region is,

Area of 80° Sector + Area of 60° Sector + Area of 40° Sector

Formula for the area of a sector is (1/2 × $radius^{2}$ × angle in radians)

= ((1 / 2) × $radius^{2}$ × 1.39626) + ((1 / 2) × $radius^{2}$ × 1.0472) + ((1 / 2) × $radius^{2}$ × 0.698132)

= ((1 / 2) × $7^{2}$ × 1.39626) + ((1 / 2) × $7^{2}$ × 1.0472) + ((1 / 2) × $7^{2}$ × 0.698132)

= 34.20837 + 25.6564 + 17.104234

= 60.969004 $cm^{2}$

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