the length of each side of a square is decreased by 20% , find the percentage change in its area

The area of a square is the width multiplied by the height. Since it is a square, the edges are all equal length, okay?

That means if we call the length of any side L, then the area can be found by multiplying L with L.

\(L*L=L^2\)

 

Now removing 20% off the length is the same as saying that 80% remains. 80 percent means 80 per 100, 80/100=0.8

So our new length is 0.8 times L.

Our new area is then \((0.8L)^2=0.8L*0.8L=0.64*L^2\)

 

This is 64% of the original area of \(L^2 \)

So 36% of the area was lost.