Answer:
Option D. The student did not use the correct formula to calculate the area of the segment
Step-by-step explanation:
step 1
Find the area of the isosceles triangle
Applying the law of sines
[tex]A=\frac{1}{2}(12^{2})sin(60\°)=62.35\ ft^{2}[/tex]
step 2
Find the area of the sector
The area of the sector is 1/6 of the area of the circle
so
[tex]A=\pi r^{2}/6[/tex]
substitute the value
[tex]A=(3.14)(12)^{2}/6=75.36\ ft^{2}[/tex]
step 3
Find the area of the segment
The area of the segment is equal to the area of sector minus the area of triangle
[tex]A=75.36\ ft^{2}-62.35\ ft^{2}=13.01\ ft^{2}[/tex]
therefore
The student did not use the correct formula to calculate the area of the segment
