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 `sqrt3 `= 1.73205]

Answer 1

Let the side of the equilateral triangle be a.

Area of equilateral triangle = 17320.5 cm²

^{sqrt3/4(s)^2 = 17320.5}

^{1.7320/4a^2 = 17320.5}

a² = 4 x 10000

a = 200 cm

Each sector is of measure 60°.

Area of sector ADEF = `60^@/360^@ xx pixxr^2`

`=1/6xxpixx(100)^2`

`=(3.14xx10000)/6`

`= 15700/3 cm^2`

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

`= 17320.5 - 3xx 15700/3`

= 17320.5-15700 = 1620.5 cm²