**Problem Statement:**

We are given an equilateral triangle of side 1. Squares are drawn on all three sides of the triangle. We need to find the area of the region enclosed by the rubber band when it stretches around the squares.

**Solution:**

To solve this problem, we'll break it down into smaller steps:

**Step 1: Find the area of each square**

Since all three squares are congruent, we only need to calculate the area of one square.

The side length of each square is equal to the side length of the equilateral triangle, which is 1.

The formula to find the area of a square is:

Area = side length * side length

Substituting the value of the side length, we get:

Area = 1 * 1 = 1

So, the area of each square is 1 square unit.

**Step 2: Find the perimeter of each square**

The perimeter of a square is the sum of the lengths of its four sides.

Since each side of the square has a length of 1, the perimeter of each square is:

Perimeter = 1 + 1 + 1 + 1 = 4

**Step 3: Find the total length of the rubber band**

The rubber band stretches around all three squares. So, the total length of the rubber band is equal to the sum of the perimeters of the three squares.

Since all three squares have the same perimeter, we can calculate the total length of the rubber band as:

Total length = 3 * Perimeter of one square

Substituting the value of the perimeter, we get:

Total length = 3 * 4 = 12

So, the total length of the rubber band is 12 units.

**Step 4: Find the area enclosed by the rubber band**

The rubber band forms a closed loop around the squares, enclosing a region.

To find the area of this region, we need to calculate the area of the outer shape formed by the rubber band.

The outer shape is a regular hexagon, which can be divided into six equilateral triangles.

The formula to find the area of an equilateral triangle is:

Area = (sqrt(3) / 4) * side length^2

Substituting the value of the side length, we get:

Area = (sqrt(3) / 4) * 1^2 = (sqrt(3) / 4)

Since the hexagon consists of six equilateral triangles, the total area of the hexagon is:

Total area = 6 * Area of one equilateral triangle

Substituting the value of the area, we get:

Total area = 6 * (sqrt(3) / 4) = (3 * sqrt(3)) / 2

So, the area enclosed by the rubber band is (3 * sqrt(3)) / 2 square units.

Therefore, the area of the region enclosed by the rubber band is (3 * sqrt(3)) / 2 square units.

3 root three