regular 12-sided polygon is inscribed in a circle of a radius r cm. Find the area (in sq.cm) of the region between the circle and the polygon.( − 2) r2(  − 3) r2(  − 1) r2None of the above

The area of the region between the circle and the polygon can be found by subtracting the area of the polygon from the area of the circle.

Step 1: Find the area of the circle The formula for the area of a circle is πr². So, the area of the circle is πr² square cm.

Step 2: Find the area of the regular 12-sided polygon A regular 12-sided polygon is also known as a dodecagon. The formula for the area of a regular polygon is (1/2) * n * r² * sin(2π/n), where n is the number of sides. So, the area of the dodecagon is (1/2) * 12 * r² * sin(2π/12) = 3r² * (2 - √3) square cm.

Step 3: Subtract the area of the dodecagon from the area of the circle The area of the region between the circle and the dodecagon is πr² - 3r² * (2 - √3) = r² * (π - 6 + 3√3) square cm.

So, the answer is None of the above.