On a square cardboard sheet of area `784 cm^(2)` , four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square not covered by the circular plates.

Explanation

`because` Area of square = 784
`:. ("side")^(2) = (28)^(2)`
`rArr` side = 28cm
since, all four are congruent circular plates.
`:.` Diameter of each circular plate = 14 cm
`:.` Radius of each circular plate = 7 cm
Now, area of one circular plate = `pir^(2) = (22)/(7)(7)^(2)`
= `154cm^(2)`
`:.` Area of four circular plates= `4 xx 154 = 616 cm^(2)`
`:.` Area of the square sheet not covered by the circular plates = `784 - 616= 168 cm^(2)`