Answer:
A. Perimeter of segment = 49 in.
B. Area of segment = 52 in².
Step-by-step explanation:
Data obtained from the question include:
Radius (r) = 24 in.
Angle at the centre (θ) = 60°
Perimeter of segment =.?
Area of segment =.?
A. Determination of the perimeter of the segment.
Perimeter of segment = length of arc + length of chord
Length of arc = θ/360 x 2πr
Length of chord = 2r x sine (θ/2)
Pi (π) = 3.14
Length of arc = θ/360 x 2πr
Length of arc = 60/360 x 2 x 3.14 x 24
Lenght of arc = 25.12 in
Length of chord = 2r x sine (θ/2)
Length of chord = 2 x 24 x sine (60/2)
Length of chord = 24 in
Perimeter of segment = length of arc + length of chord
Perimeter of segment = 25.12 + 24
Perimeter of segment = 49.12 ≈ 49 in.
B. Determination of the area of the segment.
Area of segment = Area of sector – Area of triangle.
Area of sector = θ/360 x πr²
Area of triangle = r²/2 sine θ
Area of sector = θ/360 x πr²
Area of sector = 60/360 x 3.14 x 24²
Area of sector = 301.44 in²
Area of triangle = r²/2 sine θ
Area of triangle = 24²/2 x sine 60
Area of triangle = 249.42 in².
Area of segment = Area of sector – Area of triangle.
Area of segment = 301.44 – 249.42
Area of segment = 52.02 ≈ 52 in²
