ΔLMN is an equilateral triangle. LM = 14 cm. Three sectors are drawn with vertices as centres and radius 7 cm. Find (1) A(ΔLMN) (2) Area of any one of the sectors (3) Total area of all the three sectors (4) Area of the shaded region.

ΔLMN is an equilateral triangle. LM = 14 cm. As shown in figure, three sectors are drawn with vertices as centres and radius 7 cm. Find, (1) A(ΔLMN) (2) Area of any one of the sectors. (3) Total area of all the three sectors. (4) Area of the shaded region.

Figure: each sector lies inside the triangle with its centre at a vertex; the three sectors touch one another at the midpoints of the sides; the shaded region is the part of the triangle not covered by the sectors.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

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Answer: (1) ≈ 84.87 cm² (2) ≈ 25.67 cm² (3) 77 cm² (4) ≈ 7.87 cm²

(1) \(A(\Delta LMN)=\dfrac{\sqrt3}{4}\times14^2=49\sqrt3\approx49\times1.732=84.87\) cm².

(2) Each angle of the triangle is \(60^\circ\): sector \(=\dfrac{60}{360}\times\dfrac{22}{7}\times49=\dfrac{77}{3}\approx25.67\) cm².

(3) Three sectors \(=3\times\dfrac{77}{3}=77\) cm².

(4) Shaded region \(=84.87-77=7.87\) cm² (approximately).

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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ΔLMN is an equilateral triangle. LM = 14 cm. Three sectors are drawn with vertices as centres and radius 7 cm. Find (1) A(ΔLMN) (2) Area of any one of the sectors (3) Total area of all the three sectors (4) Area of the shaded region.

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