The perimeter of the polygon is 28 cm. The length of each side is 40 mm. What is the name of the polygon?

Find using the equation the number of sides of a given polygon.

Let’s denote this number of sides by x.

According to the condition of the problem, the length of each side of this polygon is 40 mm.

Therefore, all sides of a given polygon are equal to each other.

Let’s express the side length of a given regular polygon in centimeters.

Since there are 10 millimeters in 1 centimeter, the side length of this regular polygon in centimeters is:

40 mm = 40/10 cm = 4 cm.

According to the condition of the problem, the perimeter of the polygon is 28 cm, therefore, we can draw up the following equation:

x * 4 = 28.

Solving this equation, we get:

x = 28/4;

x = 7.

Therefore, this polygon is a regular 7-gon.

Answer: This polygon is a regular 7-gon.