Question

The area of an equilateral triangle ABC is 17320.5 cm². With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and √ 3 = 1.73205]

Answer 1

Let the side of the equilateral triangle be a.

Area of equilateral triangle = 17320.5 cm²

Each sector is of measure 60°.

Area of sector ADEF = 60^o/360^o x π r²

= 1/6 x π x 100² = (3.14 x 10000)/6

=15700/3 cm²  

Area of shaded region = Area of equilateral triangle − 3 × Area of each sector

=17320.5 - 3 x 15700/3

= 17320.5 - 15700 = 1620.5 cm²