Here is a shape. The shape is made from one large square and eight identical small squares. The area of the whole shape is 108 centimeters squared. Calculate the area of the large square.
We are told that the shape which is made from one large square and eight small identical squares has a total area of 108 centimeters squared. In order to find the area of the largest square then, let’s begin by splitting the shape up.
Here is the large square. We can see that we can split this large square up into four smaller squares. And we can also see that each of these squares is the same size as the other eight identical squares. We can, therefore, count the total number of small squares that make up this shape.
There are a total of 12 small squares that make up this shape. These 12 small squares then have a combined area of 108 centimeters squared.
In order to find the area of one small square then, we can divide through by 12. 108 divided by 12 is nine. So each of the smaller squares has an area of nine centimeters squared.
We said that the largest square is made up of four of the smaller squares. We can, therefore, find the area of the large square by multiplying nine by four. Nine multiplied by four is 36.
So the area of the large square is 36 centimeters squared.