Question

A student determined that the area of the segment of c shown above is Asegment = 137.71 ft2. The student's work is shown below. Evaluate the student’s answer.

Answer 1

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

$A=\frac{1}{2}(12^{2})sin(60\°)=62.35\ ft^{2}$

step 2

Find the area of the sector

The area of the sector is 1/6 of the area of the circle

so

$A=\pi r^{2}/6$

substitute the value

$A=(3.14)(12)^{2}/6=75.36\ ft^{2}$

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

$A=75.36\ ft^{2}-62.35\ ft^{2}=13.01\ ft^{2}$

therefore

The student did not use the correct formula to calculate the area of the segment