Sector Area 5Bc283

1. **State the problem:** We need to find the area of a sector of a circle with radius $5$ meters and central angle $243^\circ$. 2. **Formula for the area of a sector:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by: $$A = \frac{\theta}{360} \times \pi r^2$$ 3. **Substitute the given values:** $$A = \frac{243}{360} \times \pi \times 5^2$$ 4. **Calculate the radius squared:** $$5^2 = 25$$ So, $$A = \frac{243}{360} \times \pi \times 25$$ 5. **Simplify the fraction:** $$\frac{243}{360} = \frac{\cancel{243}}{\cancel{360}}$$ Since $243$ and $360$ share a common factor of $9$: $$\frac{243 \div 9}{360 \div 9} = \frac{27}{40}$$ So, $$A = \frac{27}{40} \times \pi \times 25$$ 6. **Multiply the constants:** $$\frac{27}{40} \times 25 = \frac{27 \times 25}{40} = \frac{675}{40}$$ Simplify by dividing numerator and denominator by 5: $$\frac{\cancel{675} \div 5}{\cancel{40} \div 5} = \frac{135}{8}$$ So, $$A = \frac{135}{8} \pi$$ 7. **Calculate the numerical value:** $$A \approx \frac{135}{8} \times 3.1416 = 16.875 \times 3.1416 \approx 52.96$$ 8. **Final answer:** The area of the shaded sector is approximately $52.96$ square meters.