Question

35

The area of an equilateral triangle is 225V
3 sq.cm. 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.
Find the area of that part of the triangle which is not included in the circles. (Take it =
3.14 and V3 = 1.732​

Answer 1

Answer:

Area of the shaded region

= Area of an equilateral triangle -area of 3 sectors

Given : Area of equilateral ΔABC=100√3cm

2

⇒

5

3

a

2

=100√3

⇒a

2

=400

⇒a=20cm

It is given that radius is equal to half the length of the side i.e.

r=

2

a

=

2

20

=10cm

Now ,

Area of 3 sectors =3×

360

θ

×πr

2

Area of 3 sectors = 3×

360

60

×

7

22

×10×10

=

7

11

×100

=157.14cm

2

Hence the area of the shaded region

= Area of ΔABC - Area of 3 sectors

=100√3−157.14

=100×1.732−157.14

=173.2−157.14

=16.06cm

2