# ∆ 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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