Sum

\[∆\] LMN is an equilateral triangle. LM = 14 cm. As shown in the figure, three sectors are drawn with vertices as centers and radius 7 cm.

Find, A ( \[∆\] LMN)

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#### Solution

∆LMN is an equilateral triangle.

∴ LM = MN = LN = 14 cm

∠L = ∠M = ∠N = 90º Area of ∆LMN = \[\frac{\sqrt{3}}{4} \left( \text{ Side} \right)^2 = \frac{\sqrt{3}}{4} \times \left( 14 \right)^2 = \frac{1 . 732}{4} \times 196\] =84.87 cm^{2}

Concept: Areas of Sector and Segment of a Circle

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