Question 10
The area of an equilateral triangle ABC is 17320.5cm2. 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 Fig. 12.28). Find the area of the shaded region. (Use π=3.14and√3=1.73205)
ABC is an equilateral triangle.
∴∠A=∠B=∠C=60∘
There are three sectors each making 60∘.
Area of ΔABC=17320.5 cm2
⇒√34×(side)2=17320.5⇒(side)2=17320.5×41.73205⇒(side)2=4×104⇒side=200cm
Radius of the circles =2002cm=100cm
Area of the sector =(60∘360∘)×πr2cm2
=16×3.14×(100)2cm2
=157003cm2
Area of 3 sectors =3×157003=15700cm2
Area of the shaded region = Area of equilateral triangle ABC - Area of 3 sectors
=17320.5−15700cm2=1620.5cm2