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:

⇒ A_{T} = 84.87 sq.cm

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

As we know,

Here ,

⇒ A_{S} = 25.67 sq. cm

(3) Total area of all sector, A_{TS} = 3× A_{S}

⇒ A_{TS} = 3× 25.67

⇒ A_{TS} = 77.01 sq.cm

(4) Area of shaded region, A_{R} = Area of triangle – Area of all three sectors

⇒ A_{S} = A_{T} - A_{TS}

⇒ A_{S} = 84.87 – 77.01

⇒ A_{S} = 7.86 sq. cm

∴ area of shaded region is 7.86 sq. cm

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