**Problem**

A square with a side length of 2 cm is placed 20 cm in front of a concave mirror with a focal length of 10 cm. The square is positioned with its center on the axis of the mirror and its plane normal to the axis. We need to determine the area enclosed by the image formed by the mirror.

**Solution**

To solve this problem, we can follow these steps:

1. Determine the position of the image formed by the mirror.
2. Calculate the size of the image.
3. Calculate the area enclosed by the image.

Let's proceed with each step in detail.

**Step 1: Determine the position of the image**

Since the square is placed 20 cm in front of the mirror and the mirror has a focal length of 10 cm, we can use the mirror formula to find the position of the image. The mirror formula is given by:

1/f = 1/v - 1/u

where:
- f is the focal length of the mirror
- v is the distance of the image from the mirror
- u is the distance of the object from the mirror

In this case, f = -10 cm (since the mirror is concave), and u = -20 cm (negative because the object is placed in front of the mirror). Solving the equation for v, we get:

1/-10 = 1/v - 1/-20
-1/10 = 1/v + 1/20
-1/10 = (1 + v)/20

Simplifying the equation further, we have:

-1 = (1 + v)/2

Multiplying both sides by -2, we get:

2 = 1 + v

Therefore, v = 1 cm.

So, the image is formed 1 cm in front of the mirror.

**Step 2: Calculate the size of the image**

To calculate the size of the image, we can use the magnification formula:

magnification = v/u

In this case, v = 1 cm and u = -20 cm. Substituting the values, we get:

magnification = 1/-20 = -1/20

Therefore, the magnification is -1/20.

The size of the image can be calculated by multiplying the size of the object by the magnification. Since the object is a square with a side length of 2 cm, the size of the image is:

2 cm * (-1/20) = -0.1 cm

So, the size of the image is -0.1 cm.

**Step 3: Calculate the area enclosed by the image**

The area enclosed by the image is equal to the square of the size of the image. Since the size of the image is -0.1 cm, the area enclosed by the image is:

(-0.1 cm)^2 = 0.01 cm^2

Therefore, the area enclosed by the image is 0.01 square centimeters.