Area of shaded region = <em>area of circle</em> - <em>area of segment</em>
(where "segment" refers to the unshaded region)
<em>Area of circle</em> = <em>π</em> (11.1 m)² ≈ 387.08 m²
The area of the segment is equal to the area of the sector that contains it, less the area of an isosceles triangle:
<em>Area of segment</em> = <em>area of sector</em> - <em>area of triangle</em>
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130° is 13/36 of a full revolution of 360°. This is to say, the area of the sector with the central angle of 130° has a total area equal to 13/36 of the total area of the circle, so
<em>Area of sector</em> = 13/36 <em>π</em> (11.1 m)² ≈ 139.78 m²
Use the law of cosines to find the length of the chord (the unknown side of the triangle, call it <em>x</em>) :
<em>x</em> ² = (11.1 m)² + (11.1 m)² - 2 (11.1 m)² cos(130°)
<em>x</em> ² ≈ 404.82 m²
<em>x</em> = 20.12 m
Call this length the base of the triangle. Use a trigonometric relation to determine the corresponding altitude/height, call it <em>y</em>. With a vertex angle of 130°, the two congruent base angles of the triangle each measure (180° - 130°)/2 = 25°, so
sin(25°) = <em>y</em> / (11.1 m)
<em>y</em> = (11.1 m) sin(25°)
<em>y</em> ≈ 4.69 m
Then
<em>Area of triangle</em> = <em>xy</em>/2 ≈ 1/2 (20.12 m) (4.69 m) ≈ 47.19 m²
so that
<em>Area of segment</em> ≈ 139.78 m² - 47.19 m² ≈ 92.59 m²
Finally,
Area of shaded region ≈ 387.08 m² - 92.59 m² ≈ 294.49 m²
