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प्रश्न
(2) Area of any one of the sectors
उत्तर
Given,
ΔLMN is an equilateral triangle.
LM = 14 cm
Radius of the sectors (r) = 7 cm
(1) ΔLMN is an equilateral triangle. LM = 14 cm ...(Given)
Area of an equilateral triangle is `sqrt3/4 ("side")^2`.
A(ΔLMN) = `sqrt3/4 (14)^2`
A(ΔLMN) = `sqrt3/4 × 196`
A(ΔLMN) = `sqrt3 × 49`
A(ΔLMN) = 1.732 × 49
A(ΔLMN) = 84.868 ≈ 84.87 cm2
∴ The area of ΔLMN is 84.87 cm2.
(2) We know that, all the angles of the equilateral triangle are equal. Thus, ∠L = ∠M = ∠N = 60°.
Central angle (θ) = 60°
Area of sector = `θ/360 × πr^2`
= `60/360 × 22/7 × 7^2`
= `1/6 × 22 × 7`
= `(11 × 7)/3`
= `77/3`
= 25.67 cm2
∴ Area of one sector = 25.67 cm2
(3) Total area of all the three sectors = 3 × Area of one sector
= 3 × 25.67
= 77.01 cm2
(4) Area of shaded region = A(∆LMN) – total area of all three sectors
= 84.87 − 77.01
= 7.86 cm2
∴ Area of shaded region = 7.86 cm2.
(2) Area of any one of the sectors = 25.67 cm2
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