The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.
The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is
A = (θ/360) πr² sq. units
The area of the triangle with measures of two sides and an angle between them is
A = 1/2 × a × b × sinC sq. units
Where a and b are the lengths of sides and ∠C is the angle between those sides.
It is given that,
The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².
Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,
Area of the shaded region = Area of the sector - Area of the triangle
⇒ 78.6794 - 70.4956
⇒ 8.1838 cm²
Therefore, the required area of the shaded region is 8.1838 sq. cm.
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