Let's draw the scenario to better understand the problem:
For us to be able to determine the area of the field, we will be using the following formula:
[tex]\text{ Area = }ab\text{ }\frac{\text{ sin }\theta}{2}[/tex]Where,
a = 120.32 m
b = 204.61 m
θ = the angle between the two sides or the included angle = 60.881°
We get.
[tex]\text{ Area = }ab\text{ }\frac{\text{ sin }\theta}{2}[/tex][tex]\text{ = }\frac{\text{(120.32)(204.61)(Sin 60.881}^{\circ})}{\text{ 2}}[/tex][tex]\text{ = }\frac{\text{(}24,618.6752\text{)(Sin 60.881}^{\circ})}{\text{ 2}}[/tex][tex]\text{ = }(12,309.3376)(Sin60.881^{\circ})[/tex][tex]\text{ Area = 10,753.5715 }\approx\text{ 10,753.5 sq. m.}[/tex]Therefore, the area of the field is 10,753.5 sq. m.
The answer is letter C
