Question

In the given figure, ABCD is a square of side 7 cm and A, B, C, D
are centres of equal circles which touch externally in pairs. Find
the area of the shaded region.​

Answer 1

Answer:

Given:

ABCD is a square of side 7cm.

A, B, C & Dare the centres 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 centres. Since ABCD is a square, all angles are right angles and

AB = BC = CD = AD = 7cm.

Now the distance between the centres of two circles touching externally, is the sum of their radii.

Here, the radii of the equal circles = 1/2

Side of the given square = 7/2cm = 3.5cm

Each circle has been cropped by a sector of central angle = 90°.

A(Cropped cirle) = A(circle) = A(sector)

= π(3.5)² cm² – 90°/360° × π(3.5)² cm²

Also, A(square) = 7 x 7cm² = 49cm²

So, Area of the entire figure =

A(4 x croped circles) +A(square)

= (115.5 + 49)cm² = 164.5cm²