The area of the shaded region A = 44.22
What is area of circle?
The area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius 'r' is given is πr2. π is approx 3.14 or 22/7.
- Area = π × r2, where 'r' is the radius.
- Area = (π/4) × d2, where 'd' is the diameter.
- Area = C2/4π, where 'C' is the circumference.
1) Area of circle, Ac = π r^2
Ac = π (6)^2
Ac = 113.10
2) Area of triangle, At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile, the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from center point to corner) is equivalent to 6. Using the cosine law, we can calculate for the length of one side.
s^2 = 6^ + 6^2 – 2 (6) (6) cos 120
s^2 = 108
s = 10.4
Since this is an equilateral triangle therefore all sides are equal. The area for this is:
At = (sqrt3 / 4) * s^2
At = 46.77
3) Area of segment, As is given as:
As = [ (r^2) / 2 ] ( θ rad – sin θ )
As = [(6^2) / 2] (120 * π / 180 – sin 120)
As = 22.11
Therefore the area of shaded region is:
A = 113.10 - 46.77 - 22.11
A = 44.22
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