The "area" of a room is the size of the floor. Suppose you wanted to find out whether your room was really bigger than your brother's room. You'll need to measure your room, and his room. Suppose your room is ten feet long and fifteen feet wide, but his room is eleven feet long and fourteen feet wide. Yours is wider, but his is longer. How can you tell which is really the biggest room?
Imagine that you had a stack of pieces of paper one foot long by one foot wide. How many of those pieces would fit in your room? How many would fit in his? Would you agree that whichever room would hold more pieces of paper would be the bigger room?
Well, you can see that you could lay ten pieces of paper along one side of your room, because it's ten feet long. And you could lay another row next to that one, and then another row, and another, up to fifteen rows. Your brother would be able to fit in eleven pieces of paper along one side of his room, but he would only be able to fit in fourteen rows.
You find the area by multiplying the length (how long it is) by the width (how wide it is). Your room is 10 x 15 = 150 square feet. Your brother's room is 11 x 14 = 154 square feet. Ha! Just as you always suspected, his room is bigger. How unfair! (But both of your rooms are larger than the average slave cabin or the average Navajo hogan, where whole families lived.)