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. 

Area of a triangle can be determined using the equation:

In order to find the area of a triangle, we multiply the base by the height, and then divide by 2.

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

Multiply both sides by two, which allows us to eliminate the two from the left side of our fraction.

The left-hand side simplifies to:

The right-hand side simplifies to:

Now our equation can be rewritten as:

Next we divide by 8 on both sides to isolate the variable:

Therefore, the height of the triangle is .

The area of a triangle is found by multiplying the base times the height, divided by 2. 

Given that the height is 9 inches, and the base is one third of the height, the base will be 3 inches.

We now have both the base (3) and height (9) of the triangle. We can use the equation to solve for the area.

The fraction cannot be simplified.

The formula for the area of a triangle is . In this case, the base is 11 and the height is 9. So, we're multiplying

The area of triangle is found using the formula

.

Provided with the base and the height, all we need to do is plug in the values and solve for A. 

.

Since this is asking for the area of a shape, the units are squared.

Thus, our final answer is . 

The area of triangle is found using the formula

.

Provided with the base and the height, all we need to do is plug in the values and solve for A. 

.

Since this is asking for the area of a shape, the units are squared.

Thus, our final answer is  . 

The area of triangle is found using the formula

.

Provided with the base and the height, all we need to do is plug in the values and solve for A. 

. 

Since this is asking for the area of a shape, the units are squared.

Thus, our final answer is .