A pentagon has a perimeter of 20ft. If every side is halved, find the new perimeter

How to get this

A pentagon has 5 sides. If each side is the same length, then each side is 20/5 = 4 feet long. That halves to 4/2 = 2 feet. Each side is now 2 feet long, and there are 5 total sides, so 2*5 = 10 feet is the new perimeter.

A shortcut is to simply divide the perimeter in half to get 20/2 = 10. The reason why this works is because the perimeter is the sum of all the sides, which are all being cut in half.

Algebraically, if we had the five sides a,b,c,d,e then

P = a+b+c+d+e

is the perimeter

Cutting each side in half gives

0.5*a+0.5*b+0.5*c+0.5*d+0.5*e = 0.5*(a+b+c+d+e) = 0.5*P

showing that we've cut the perimeter in half.

could you provide figure.