Answer:
The area of the unshaded segment of Circle G is approximately 22.47 square inches
Explanation:
To find the area of the segment of Circle G, we need to subtract the area of the triangle formed by the radius and chord from the area of the sector.
Firstly, let's find the area of the sector:
The formula for the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius.
In this case, the central angle is 120° (as the triangle formed is an equilateral triangle), and the radius is 7 inches.
So, the area of the sector is A = (120/360) * π * 7² = (1/3) * π * 49.
Next, let's find the area of the triangle:
The formula for the area of an equilateral triangle is A = (√3/4) * s², where s is the length of a side.
In this case, since the radius is also a side of the equilateral triangle, the length of a side is 7 inches.
So, the area of the triangle is A = (√3/4) * 7² = (√3/4) * 49.
Now, let's subtract the area of the triangle from the area of the sector to find the unshaded area of the segment:
Unshaded area = (1/3) * π * 49 - (√3/4) * 49.
Calculating this expression, we get:
Unshaded area ≈ 22.47 square inches.
Therefore, the area of the unshaded segment of Circle G is approximately 22.47 square inches.