find the area of the shaded region 7cm
Answers
Answer:
Find the area of a shaded region in the given figure, where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use π =
Step-by-step explanation:
⇒ Here, Radius of circle r=7cm
⇒ Area of circle =πr
2
=
7
22
×(7)
2
=154cm
2
⇒ Side of equilateral triangle is 14cm.
⇒ Area of equilateral triangle =
4
3
×(side)
2
⇒ Area of equilateral triangle =
4
3
×(14)
2
⇒ Area of equilateral triangle =
4
1.73
×196=84.87cm
2
⇒ ∠A=60
o
[ Angle of equilateral triangle ]
∴ θ=60
o
⇒ Area of sector =
360
o
θ
×πr
2
⇒ Area of sector =
360
o
60
o
×
7
22
×(7)
2
∴ Area of sector =25.66cm
2
⇒ Area of shaded region = (Area of circle + Area of equilateral triangle ) - 2×Area of sector
⇒ Area of shaded region =(154+84.87)−51.32=187.55cm
2