Based on the radius of the being 4 units and the area of the equilateral triangle, the area of the shaded area is 32.85 units².
<h3>What is the area of the shaded area?</h3>
First, find the area of the triangle.
The center of a triangle divides the median into a 2:1 ratio which means that the radius can be found as:
Radius = 1/3 x Area of Equilateral triangle
4 = 1/3 x (√3/ 2)a
a can be worked out to be:
= 8√3
The area of the triangle is:
= (√3 / 4) x a²
= (√3 / 4) x (8√3 )²
= 83.14 units ²
The area of the circle is:
= π x radius²
= 22/7 x 4 x 4
= 50.29 units²
The area of the shaded area is therefore:
= 83.14 - 50.29
= 32.85 units²
In conclusion, the area of the shaded area is 32.85 units².
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