Given: In equilateral triangle LMN, LM =14 cm,
radius of sectors (r) = 7 cm
i. ∆LMN is an equilateral triangle.
∴ (∆LMN) = √3/4 LM2
= √3/4 x 142
= 49 x 1.732
= 84.868
= 84.87 cm2
.∴ (∆LMN) = 84.87 cm2
ii. Central angle (θ) = 60° …[Angle of an equilateral triangle]
∴ Area of one sector = 25.67 cm2
iii. Total area of all three sectors = 3 × Area of one sector
= 3 × 25.67
= 77.01 cm2
∴ Total area of all three sectors = 77.01 cm2
iv. 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.