Question

find the area of the shaded region in the figure where a circular arc of radius 3 cm has been drawn with vertex o of an equilateral triangle oab of side 6 cm as center​

Answer 1

    Since ROQ is a diameter, therefore, ∠RPQ=90o

            In rt ∠dΔPRQ RQ2=RP2+PQ2

            ⇒ RQ2=72+242=49+576=625

            ⇒ RQ=625−−−√=25cm

            Therefore, Radius r=12RQ=252cm

            Area of the semi circle =12πr2=12×227×252×252cm2

            =687528cm2

            and area of ΔRPQ=12×RP×PQ

            =(12×7×24)cm2=84cm2

            Area of the shaded region

            = Area of the semi circle – Area (Δ RPQ)

            =(687528−84)cm2=(6875−235228)cm2

            =452328cm2