Final answer:
The area of the shaded region in an equilateral triangle that encloses a circle with a radius of 2 units and a triangle area of 8√3 square units, is given by subtracting the area of the circle (4π square units) from the area of the triangle, which results in: 8√3 - 4π square units.
Step-by-step explanation:
The subject of this question is geometry. We'll need to find the area of the equilateral triangle first, subtract the area of the circle from it to find the shaded region.
The given area of the equilateral triangle is 8√3 square units. And the radius of the circle is 2 units.
The formula to find the area of a circle is πr². So, plugging in the given radius, the area of the circle is π(2)² = 4π square units.
Subtracting the area of the circle from that of the triangle, the area of the shaded region is: 8√3 - 4π square units.
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