Question

The area of an equilateral $\Delta ABC$ is 17320.5 $c{m}^2$ with each vertex of the triangle as centre a circle is drawn with radius equal to half the length of the side of triangle. Find the area of the shaded region. $(\pi =3.14,\sqrt{3}=1.73205)$ [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks

Area of shaded region = area of $\Delta ABC$ - 3 (Area of sector BPR)

Let 'a' be the side of the equilateral $\Delta$ABC.

$\frac{a^2\sqrt{3}}{4}=17320.5$

$a=200cm$

Radius of the circles
$=\frac{1}{2}\times a=100cm$

$\therefore$ Required area
$=17320.5-3[\frac{60}{360}\times \pi \times {100}^2]$

$=1620.5c{m}^2$