Math Trivia : Two sectors

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The figure shows two sectors with 12 cm in radius and 30 degrees of central angles. Find the area of the shadow. Pi is assumed to be 3.




Answer
36 cm2

Since △ABO and △CDO are congruent,
(Area of shadow area) = (figure ACDO) - (△ABO)
                                        = (figure ACDO) - (△CDO)
                                        = sector ACO 
                                        = 12 × 12 × 3 × 30/360 = 36cm2.