The area is the square of the side 1½²=(3/2)²=9/4=2¼ square feet.

The picture below should help.

The square poster is shown as the big square with black and red sides. The red square measures 1 foot a side, and the dotted lines inside it show that it’s made up of 4 smaller squares, each with quarter of the area of the red square, which measures 1 square foot. So each smaller square has an area of ¼ square foot because there are 4 inside the red square. We add ½ foot to the red square to make it the size of the poster. And we can see how much bigger it is than the red square. If we count all the smaller squares including the ones in the red square we have 9. Each square has an area of ¼ square foot, so 9 smaller squares have a total of 9 quarters, which we write as 9/4 square feet. 4 goes into 9 twice with a remainder of 1, that is, one quarter left over so the area of the poster is 2¼ square feet (2 plus one quarter). In other words, we have enough smaller squares to fill the red square twice with one smaller square left over.

I hope this helps you to understand.