Answer:
The area of the circle enclosed by line PL and arc PL is approximately 37.62 square units
Step-by-step explanation:
The given parameters in the question are;
The radius of the circle, r = 11
The length of the chord PL = 16
The measure of angle ∠PAL = 93°
The segment of the circle for which the area is required = Minor segment PL
The shaded area of the given circle is the minor segment of the circle enclosed by line PL and arc PL
The area of a segment of a circle is given by the following formula;
Area of segment = Area of the sector - Area of the triangle
In detail, we have;
Area of segment = Area of the sector of the circle that contains the segment) - (Area of the isosceles triangle in the sector)
Area of a sector = (θ/360)×π·r²
Where;
r = The radius of the circle
θ = The angle of the sector of the circle
Plugging in the the values of <em>r</em> and <em>θ</em>, we get;
The area of the sector enclosed by arc PL and radii AP and AL = (93°/360°) × π × 11² ≈ 98.2 square units
Area of a triangle = (1/2) × Base length × Height
Therefore;
The area of ΔAPL = (1/2) × 16 × 11 × cos(93°/2) ≈ 60.58 square units
∴ The area of the segment PL ≈ (98.2 - 60.58) square units = 37.62 square units
Therefore, the area of the shaded segment PL ≈ 37.62 square units
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