A wire bent in a shape of a regular pentagon with each side 4cm is opened up and rebent into a shape of a square. What is the length of the side of the square? = __________cm
 

Dear Student,
Length Of Wire = Perimeter of regular pentagon.
Now, perimeter of pentagon = 5$\times$Side
Side = 4cm
Hence, perimeter of the pentagon = Length of wire = 20cm
Now, it needs to be rebent as a square.
Perimeter Of Square = Length Of wire.
But, perimeter of square = 4$\times$Side
Hence Side Of Square = $\frac{Length Of Wire}{4}=\frac{20}{4}=5cm$
Regards.