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Byju's Answer
Standard VIII
Mathematics
Area of Combined Shapes
ABC is the eq...
Question
ABC is the equilateral triangle inscribed in a circle of radius 4 cm with center O. Find the area of shaded region
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Solution
We have,
R
=
4
c
m
∴
A
B
=
B
C
=
C
A
=
R
√
3
=
4
√
3
cm .............
[
∵
R
=
2
3
h
a
n
d
h
=
√
3
2
a
∴
R
=
a
√
3
]
∠
A
O
C
=
∠
A
B
C
=
2
×
60
∘
=
120
∘
∴
Required area =
1
3
(Area of the circle - Area of
Δ
ABC)
⇒
Required area =
1
3
[
π
R
2
−
√
3
4
×
(
s
i
d
e
s
)
2
]
⇒
Required area =
1
3
[
16
π
−
√
3
4
×
(
4
√
3
)
2
]
⇒
Required area =
1
3
(
16
π
−
12
√
3
)
c
m
2
=
4
3
(
4
π
−
3
√
3
)
c
m
2
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Q.
In the given figure, an equilateral triangle has been inscribed in a circle of radius 4 cm. Find the area of the shaded region.