AREAS RELATED
TO CIRCLE
shaded portion
Sol.
A
B
C
ar (shaded region) =
ar (ΔABC)
ar (3 sectors)
–
3 ar (1 sector)
ar (ΔABC)
=
17320.5 cm2
From area, let us find side of the equilateral triangle
What is the formula to find area of an equilateral triangle?
4
side2
ar (ΔABC)
=
(side)2
4
∴
(side)2
4
=
∴
1.73205
4
(side)2
17320.5
=
17320.5
∴
173205
4 × 100000
(side)2
=
173205
4 × 10
A
B
C
ar (shaded region) =
ar (ΔABC)
–
3 ar (1 sector)
∴
173205
4 × 100000
(side)2
=
173205
4 × 10
∴
(side)2
=
173205 × 4 × 100000
10 × 173205
=
4 × 10000
side
=
2 × 100
∴
side
=
200 cm
✔
Sol.
B
C
ar (shaded region) =
ar (ΔABC)
–
3 ar (1 sector)
What is the formula to find area of sector?
Side = 200 cm
?
Radius (r)
=
1
2
× Side
=
1
2
× 200
∴
Radius (r)
=
100
✔
θ
360
πr2
?
60°
Central angle (θ) = 60°
✔
ar (3 sectors) =
θ
360
πr2
3 ×
=
3 ×
60
360
100
100
3.14
We know that, angle of an equilateral triangle = 60°
ar (3 sectors)
✔
Sol.
A
ar (shaded region) =
ar (ΔABC)
–
3 ar (1 sector)
C
=
3 ×
60
360
100
100
3.14
ar (3 sectors)
6
1
1
2
=
1
2
314
100
100
100
157
=
15700 cm2
✔
✔
Sol.
A
B
ar (shaded region) =
ar (ΔABC)
–
3 ar (1 sector)
✔
✔
B
C
ar (shaded region) =
ar (ΔABC)
–
3 ar (1 sector)
=
17320.5
–
15700
3 ar (1 sectors) = 15700 cm2
=
1620.5 cm2
Area of the shaded portion is 1620.5 cm2
∴
Sol.
A