Question

A circle with a radius of one unit is inscribed in an equilateral triangle with an area of 4√3 square units. Determine the exact area of the shaded region.

4√3 - 2pi square units
4√3 + 2pi square units
4√3 - pi square units
4√3 + pi square units

Answer 1

the answer is 4squareroot3 - pi

Answer 2

4√3 -π square units

Explanation:

The triangle area is given. The area of the circle is πr², where r=1, so is π square units.

If the shaded area is the difference, then its area is ...

... 4√3 - π

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Comment on the problem statement

Normally, when a figure is "inscribed", the size of the inscribed figure is limited by the enclosing figure. Here, the circle is not "inscribed" in the triangle, as the triangle is larger than would be required for an inscribed circle of radius 1.