Answer: ≈ 13.98 in2
Step-by-step explanation:
A segment of a circle is a region bounded by an arc and its chord.
To determine the area of the segment, begin by finding the area of the sector defined by the central angle.
A sector of a circle is a region bounded by two radii of the circle and their intercepted arc.
The formula for the sector area is A = πr2 (m∘/360∘).
It is given in the figure that central angle MNO is a right angle. So, m∠MNO = 90∘. It is also given that r = 7 in.
Substitute the given values into the formula and simplify.
A = π(7)2 (90∘/360∘) = 49/4π in2
Find the area of △MNO.
Since the radii in a circle are congruent, NO = NM = 7. To find the area of △MNO, use the formula for the area of a triangle, A = 1/2bh.
Substitute 7 for b and 7 for h, then simplify.
A = 1/2 (7) (7) = 24.5 in2
The area of the segment is the difference between the two areas, the area of the sector and the area of the triangle.
A = 49/4π − 24.5 ≈ 13.98 in2
Therefore, the area of segment MNO is ≈ 13.98 in2.
