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Question

In the given figure, if ΔOAB≅ΔOFE≅ΔOCD, OD = 3 cm, DC = 6 cm OC = 5 cm, then area of the shaded portion is

A
14cm2
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B
214cm2
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C
67cm2
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D
614cm2
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Solution

The correct option is D 6√14cm2 Given: ΔOAB≅ΔOFE≅ΔOCD We know that the areas of congruent triangles are equal. ∴Ar(ΔOAB)=Ar(ΔOFE)=Ar(ΔOCD) …..(i) Semiperimeter, (s) of ΔOCD=OD+DC+OC2 =3+6+52 (Given) =7cm By Heron’s formula, area of ΔOCD=√s(s−a)(s−b)(s−c) =√7×(7−3)×(7−6)×(7−5) =√7×4×1×2 =2√14cm2 ∴ Area of shaded portion = 3× Area of ΔOCD [From (i)] =3×2√14 =6√14cm2 Hence, the correct answer is option (d).

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