Q. 134.0( 11 Votes )

∆ LMN is an equilateral triangle. LM = 14 cm. As shown in figure, three sectors are drawn with vertices as centre and radius7 cm. Find,



(1) A (Δ LMN)

(2) Area of any one of the sectors

(3) Total area of all three sectors

(4) Area of shaded region

Answer :

(1) Side of triangle = LM = a = 14 cm


Since Δ LMN is an equilateral triangle, so the area of the triangle is given by:




AT = 84.87 sq.cm


(2) Angle subtended by the corner = θ = 60°


As we know,



Here ,



AS = 25.67 sq. cm


(3) Total area of all sector, ATS = 3× AS


ATS = 3× 25.67


ATS = 77.01 sq.cm


(4) Area of shaded region, AR = Area of triangle – Area of all three sectors


AS = AT - ATS


AS = 84.87 – 77.01


AS = 7.86 sq. cm


area of shaded region is 7.86 sq. cm


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