(1) Given LMN is an equilateral triangle .

LM = 14 cm

Area of LMN = (√3/4)a^{2}

Here a represents the side of equilateral triangle.

a = 14

Area of LMN = (√3/4)×14^{2}

= 49√3

= 84.87cm^{2}

Hence area of LMN is 84.87cm^{2}

(2) Since LMN is equilateral, L = M = N = 60˚

= 60˚

Given r = 7

Area of sector = (/360)r^{2}

Area of sector = (60/360)×22/7×7^{2}

= 11×7/3

= 25.67cm^{2}

Hence area of one sector = 25.67cm^{2}

(3)Total area of 3 sectors = 3×area of one sector

= 3×25.67

= 77.01cm^{2}

Hence total area of 3 sectors is 77.01cm^{2}.

(4)Area of shaded region = Area of LMN – Area of 3 sectors

= 84.87 – 77.01

= 7.86cm^{2}

Hence area of shaded region is 7.86cm^{2}.