Question

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?

Answer 1

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