In the figure below, each curved line is an arc of a circle centered at a vertex of the triangle.

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Solution

Arc ADC is an arc of the circle whose centre is the vertex B of the equilateral triangle ABC.

∴ Radius of the circle with ADC as an arc = 4 cm

Each angle of an equilateral triangle = 60°

∴ ∠ABC = 60°

Central angle made by the arc is 60°, which is of 360°.

Length of the arc ADC = of the perimeter of the circle

= × 2π × 4 cm

= cm

Similarly, length of the arc AEB = length of the arc BFC = cm

Perimeter of the figure = Length of the arc AEB + Length of the arc BFC + Length of the arc ADC

=

= 3 × cm

= 4π cm

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