A strip with sides of 3 cm and 1 cm was cut from a rectangle with sides of 5 cm and 3 cm. Find the area of the remaining part.

Find the area of ​​the remainder
Let’s write down the known data:

Given a rectangle;
Initially, it was a = 5 cm and b = 3 cm, where a and b are the sides of the rectangle;
Cut from the sides of the rectangle 3 cm and 1 cm;
After a certain cm was cut off, the sides of the rectangle became: a = 5 cm – 3 cm = 2 cm and b = 3 cm – 1 cm = 2 cm.
After the done actions, we got that the sides of the rectangle are equal to a = 2 cm and b = 2 cm. Since the sides of the rectangle are equal, we got not a rectangle, but a square.

So, we need to find the area of ​​a square with a side a = 2 cm.

Find the area of ​​a square
Let’s write the formula for the area of ​​a square:

S = a ^ 2, where a is the side of the square.

Square properties:

All sides of a square are equal;
The diagonals of the square are equal and perpendicular;
the diagonals are the bisectors of its corners;
The diagonals divide the square into 4 isosceles triangles.
In order to find the area of ​​a square, you need to substitute the known values ​​into the formula for the area of ​​a square and calculate its value. That is, we get:

S = a ^ 2 = (2 cm) ^ 2 = 2 ^ 2 cm ^ 2 = 4 cm ^ 2;

From this, we found that the area of ​​the square is S = 4 cm ^ 2. This means that the area of ​​the remaining part is 4 cm ^ 2.