Question

In fig. ABCD is a square of side 14cm. with centre A,B,C and D. four

circles are drawn such that each circle touch externally two of the

remaining three circles. Find the area of the shaded region​

Answer 1

Answer:

42cm^2

Step-by-step explanation:

Since square has all angles 90°

Area of shaded region

= area of square ABCB

- area of 4 quardant of circles

Area of square ABCD

Given side of square = 14 cm

Area of square = Side × Side

= 14cm × 14cm

= 196 cm^2

Area of 4 quadrants of circles1/

In the question,figure shows symmetry

Therefore,radius of circle will be equal.

In every single figure radius = Side of square ÷ 2

= 14÷2

= 7

So, radius = r = 7cm

Now,

Area of 1 quadrant = 1/4 × area of circle

= 1/4 ×πr^2

= 1/4 × 22÷7 ×( 7^2)

= 1/4 × 22÷7 × (7×7)

= 1/4 × 22 × 49

= 154÷4 cm^2

Area of 4 quardants = 4×area of quadrant

= 4× 154÷4

= 154 cm^2

Area of shaded region= area of square

- area of quardrant

= 196 - 154

= 42 cm^2

Hence,area of shaded region = 42 cm^2

Hope it helps you,

Thank you