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2 answers:
Answer:
Looking at the graphic, we see radius OA = 8 inches and chord AB = 8 inches and Line AE = one half of chord AB = 4 inches
From the Pythagorean Theorem, we can then calculate the APOTHEM (Line OE) as: OE^2 = OA^2 - AE^2
OE^2 = 8^2 - 4^2 OE^2 = 64 -16 OE^2 = 48
OE = 6.9282032303 inches
Angle AOE = arc tangent (AE / OE)
Angle AOE = arc tangent (4 / 6.9282032303)
Angle AOE = 30 degrees and Angle AOB = (2 * AOE) = 60 degrees
The area of the sector (red area + green area) = (Angle AOB / 360) * PI * radius^2
Sector Area = (0.1666666667) * PI * 64
Sector Area = 33.5103216067 sq inches
Red Triangle Area = AE * OE = 4 * 6.9282032303 = 27.7128129212 sq inches
Segment Area = Sector Area - Red Triangle Area =
Segment Area = 33.5103216067 -27.7128129212
Segment Area = 5.7975086855 sq inches
Source: https://www.1728.org/circpart.htm
Step-by-step explanation:
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