37. In the given figure, ABCD is a square of side 7 em and A, B, C, D
are centres of equal circles which touch externally in pairs. Find
the area of the shaded region.
Answers
Answer:
164.5 cm*2
Step-by-step explanation:
Given:
ABCD is a square of side 7cm.
A, B, C & D are the centers of four equal circles each touching two other, externally.
To find:
The area of the entire figure.
Solution:
AB,BC,CD & AD are the distances between the respective centers.
Since ABCD is a square, all angles are right angles and
AB=BC=CD=AD=7cm.
Now the distance between the centers of two circles touching externally, is the sum of their radii.
Here, the radii of the equal circles=
2
1
Side of the given square =
2
7
cm=3.5cm.
Each circle has been cropped by a sector of central angle =90
o
.
∴ A(Cropped cirle) = A(circle) − A(sector)
=π(3.5)
2
cm
2
−
360
0
90
o
×π(3.5)
2 cm *2
Also, A(square) =7×7cm *2
=49cm *2
So, Area of the entire figure= A(4 × croped circles)+A(square)
=(115.5+49)cm * 2
=164.5cm *2