Given is

The circle is given by the equation x² + y² − 4x + 2y − 11 = 0. Calculate the area of the regular hexagon inscribed in this circle.

Final Answer:

S =  41.5692

Step-by-step explanation:

x2+y2−4x+2y−11=0 (x−x0​)2+(y−y0​)2 = r2 (x − 2)2 + (y + 1)2 − 16 = 0 (x − 2)2 + (y + 1)2 = 16  r=16​=4 a=r=4  S1​=43​​⋅ a2=43​​⋅ 42=4 3​≐6.9282  S=6⋅ S1​=6⋅ 6.9282=24 3​=41.5692

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