The area of an equilateral triangle is 49√3 cm^2. Taking each angular point as centre,a circle is described with radius equal to half the length of the side of the triangle .Find the area of the portion in the triangle not included in the circles
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The correct option is B
7.77
c
m
2
.
A
r
e
a
=
49
√
3
c
m
2
⇒
√
3
4
a
2
=
49
√
3
⇒
a
2
=
49
×
4
⇒
a
=
14
c
m
Thus, radius of each circle is 7 cm
Now, Required area
=
A
r
e
a
o
f
Δ
A
B
C
−
3
×
(Area of a sector of angle
60
∘
in a circle of radius 7 cm)
=
[
49
√
3
−
3
(
60
360
×
22
7
×
7
2
)
]
c
m
2
=
[
49
√
3
−
77
]
c
m
2
=
[
49
×
1.73
−
77
]
c
m
2
=
7.77
c
m
2
.
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