Q13 of 52 Page 154

∆ 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

(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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