find the area of the shaded part
Answers
Answer:
Area of shaded region =
= 107/14 cm^2
= 7.642875 cm^2
Step-by-step explanation:
From fig.
AD = BC = 4 cm
AB = CD = 3 cm
Diameter of circle = AC
By Pythagoras Theorem in right triangle ABC ( since <ABC = 90°),
(AC)^2 = (AB)^2 + (BC)^2
(AC)^2 = (3)^2 + (4)^2
(AC)^2 = 9 + 16
(AC)^2 = 25
AC = √25 = 5 cm
Hence,diameter of circle (d) = 5 cm
Radius of circle (r) = d/2 = 5/2 cm
NOW,
Area of shaded region = Area of circle - Area of square ..(1)
Area of circle = πr^2
= 22/7 × 5/2 ×5/2
= (11×5×5)/(7×2)
= 275 / 14 cm^2
Area of rectangle = l × b
= 4 × 3
= 12 cm^2
From eq.(1) , we get
Area of shaded region = 275/14 - 12
= ( 275 - 168 ) / 14
= 107 / 14 cm^2
= 7.642857 cm^2 (approx.)