Lesson 1: growing and shrinking

han has a thin rectangular sheet of paper. its area is 450 square inches. he folds it into thirds, and then he folds the resulting rectangle into thirds again.

1.) han believes that after two rounds of folding, the visible area of the folded paper will be 150 square inches or one-third of the original area. do you agree? explain your reasoning.

2.) what is the visible area of the paper, in square inches, after 4 rounds of folding? explain or show your reasoning.

Step-by-step explanation:

Here, the initial area of the sheet  = 450 sq inches.

After folding the sheet in to thirds ONCE :

The area of the each rectangle so formed   =   =  150 sq. inches

So, the area of each rectangle  = 150 sq inches

After folding the sheet in to thirds TWICE :

The area of the each rectangle so formed   =   =  50 sq. inches

So, the area of each rectangle  = 50 sq inches

So, as we can see after two rounds of folding, we get in total 9 rectangles.

The area of each rectangle so formed   =   50 sq inches.

50 sq inches  = of the total area.

Hence, the given statement is not true.