In the figure below, the curved lines are all arcs of circles centred on the vertices of the triangle.

What is the area of this figure?

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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 = 60°

Area of the sector, ABCD =

Similarly, area of the sector, ABFC = area of the sector, AEBC =

Area of figure = Area of the sector, ABCD + Area of the sector, ABFC + Area of the sector, AEBC

=

= (8 × 3.14) cm²

= 25.12 cm²

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In the figure below, the curved lines are all arcs of circles centred on the vertices of the triangle. What is the area of this figure?

In the figure below, the curved lines are all arcs of circles centred on the vertices of the triangle.

What is the area of this figure?