Answer:
Step-by-step explanation:
Area of a sector is expressed as [tex]\frac{\theta}{360^{0} }*\pi r^{2}[/tex]
Before we can get the area of the circle, we need to find its radius. The radius of the circle can be derived from the equation of the circle given.
[tex](x+3.5)^{2} + (y-2.82)^{2} =25[/tex]
The general form of equation of a circle is given as [tex](x-a)^{2} + (y-b)^{2} =r^{2}[/tex] where r is the radius of the circle. Comparing the general equation to the given equation to get the radius r;
[tex]r^{2} = 25\\ r = \sqrt{25}\\ r =5[/tex]
The radius of the circle is 5
Given the angle subtended by the sector of the circle to be 52°,
Area of the sector = [tex]\frac{52}{360^{0} }*\pi *5^{2}[/tex]
[tex]= \frac{52}{360^{0} }*25\pi\\= 0.144 *25 \pi[/tex]
[tex]= 0.144 * 25(3.14)\\= 0.144*78.5\\= 11.34units^{2}[/tex]
This gives the required area of the sector to nearest hundredth
