Matt looks at the architectural plan of a four-walled room in which the walls meet each other at right angles. The length of one wall in the plan is 19 inches. The length of the diagonal of the floor of the room in the plan is approximately 20.62 inches. Is the room in the shape of a square?

The room is not in the shape of a square

Step-by-step explanation:

Diagonal of a square shape

Suppose we have a square of side length a. The diagonal of the square is the hypotenuse of a right isosceles triangle of legs a. Thus the diagonal is calculated as:

The length of one wall in the plan is a=19 inches, thus the diagonal of the possible square would be:

But we also know the length of the diagonal of the floor of the room in the plan is 20.62 inches.

Thus, the room is not in the shape of a square

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm

you need to rotate this triangle about the origin 270 degrees clockwise to create the full square.