The area of a square is represented by the equation .

Therefore the area of this square is .

The area of Square A is 5 * 5, or 25 m².  

Since each of Square B's sides is 2 meters longer, the sides measure 7 meters. Therefore, the area of square B is 49 m².  

Subtract to find the difference in areas:

The area of a square can be found as follows:

Where:

So we can write:

The area of a square is found by multiplying one side by itself.

We are given the side length, allowing us to solve.

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

The area of a trapezoid can be determined using the equation .

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

The area of a triangle is found by multiplying the base by the height and dividing by two:

In this problem we are given the base, which is , and the area, which is .  First we write an equation using  as our variable.

To solve this equation, first multply both sides by , becuase multiplication is the opposite of division and therefore allows us to eliminate the .

The left-hand side simplifies to:

The right-hand side simplifies to:

So our equation is now:

Next we divide both sides by , because division is the opposite of multiplication, so it allows us to isolate the variable by eliminating .

So the height of the triangle is .

The area of a triangle is one half the product of its base and its height - in the above diagram, that means

.

Substitute , and solve for .

From this shape we are able to see that we have a square and a triangle, so lets split it into the two shapes to solve the problem. We know we have a square based on the 90 degree angles placed in the four corners of our quadrilateral. 

Since we know the first part of our shape is a square, to find the area of the square we just need to take the length and multiply it by the width. Squares have equilateral sides so we just take 5 times 5, which gives us 25 inches squared.

We now know the area of the square portion of our shape. Next we need to find the area of our right triangle. Since we know that the shape below the triangle is square, we are able to know the base of the triangle as being 5 inches, because that base is a part of the square's side. 

To find the area of the triangle we must take the base, which in this case is 5 inches, and multipy it by the height, then divide by 2. The height is 3 inches, so 5 times 3 is 15. Then, 15 divided by 2 is 7.5. 

We now know both the area of the square and the triangle portions of our shape. The square is 25 inches squared and the triangle is 7.5 inches squared. All that is remaining is to added the areas to find the total area. Doing this gives us 32.5 inches squared.