How to find the Relation between Areas Inside a Square
Find the relation between shaded areas inside a square, which is separated by three semicircle
The figure shows a square. Three semicircles are drawn inside the square and divided into six parts. Then find the relation between areas Inside a square (Blue area: Red area)
![Find the relation between shaded areas inside a square, which is separated by three semicircle](https://aplusreach.com/wp-content/uploads/2021/12/How-to-find-the-Relation-between-Areas-Inside-a-Square-1-1024x683.jpg)
Solution
We can find the relation between areas using symmetry
![We can find the relation between areas using symmetry](https://aplusreach.com/wp-content/uploads/2021/12/How-to-find-the-Relation-between-Areas-Inside-a-Square-2-1024x683.jpg)
From the above figure
shaded areas are equal (red = blue)
So we can interchange these areas then we get a figure like this
![](https://aplusreach.com/wp-content/uploads/2021/12/How-to-find-the-Relation-between-Areas-Inside-a-Square-3-1024x683.jpg)
Let the sides of the square = 2x, then
From figure
Blue area = ½ πx²
and, Red area = 4x² – ½πx²
So
Blue Area / Red Area = ½πx² / (4x² – ½πx²)
so, Blue area: Red Area = ½π: 4 – ½ π
Thus, Blue area: Red Area = π: 8 – π
Relation between shaded areas is π: 8 – π