Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches two pieces. Find the area of the portion enclosed between these pieces.

Explanation

Given that, four circular cardboard piaces arc placed on a paper in such a way that each piece touches other two pieces.
Now, we join centre of all four circles to each other by a line segment since, radius of each circle is 7 cm.
So, `AB = 2 xx` Radius of circle
= `2xx7 = 14 cm`
`rArr AB = BC = CD = AD = 14 cm`
which shows that , quadrilateral ABCD is a square with each of its side is 14 cm.
we know that, each angle between two adjacent sides of a square is `90^(@)`
`:.` Area of sector with `angleA = 90^(@)`
= `(angleA)/(360^(@))xxpir^(2) = (90^(@))/(360^(@))xxpixx(7)^(2)`
= `(1)/(4)xx(22)/(7)xx49= (154)/(4)= (77)/(2)`
= `38.5cm^(2)`
`:.` Area of each sector = `4xx` Area of sector with `angleA`
= `4xx38.5`
= ` 154 cm^(2)`
and area of square ABCD = `("side of square")^(2)`
= `(14)^(2) = 196 cm^(2)` [`:.` area of square = `("side")^(2)` ]
So, area of shaded region enclosed between these pieces = Area of square ABCD - Area of each sector
= ` 196 - 154`
` 42 cm^(2)`
Hence, required area of the portion enclosed between these pieces is `42 cm^(2)` .