**Introduction:**
To find the area enclosed by the rubber band around the squares drawn on the sides of an equilateral triangle, we can divide the problem into two parts. First, we calculate the area of the three squares, and then we subtract the areas of the overlapping regions to obtain the final result.

**Calculating the Area of the Squares:**
Since the sides of the equilateral triangle have length 1, the squares drawn on the sides will also have sides of length 1. The area of a square is equal to the square of its side length, so the area of each square is 1 * 1 = 1 square unit.

**Calculating the Overlapping Regions:**
To determine the area of the overlapping regions, we need to consider the points where the rubber band intersects with the squares. Let's refer to these points as A, B, and C, corresponding to the vertices of the equilateral triangle.

* Point A: The rubber band intersects with two squares at point A. Let's call the points where it intersects as A1 and A2.
- Triangle A1A2C is a right-angled triangle with legs of length 1 and hypotenuse of length √2 (diagonal of the square). Therefore, the area of this triangle is (1 * 1) / 2 = 0.5 square units.

* Point B: The rubber band intersects with two squares at point B. Let's call the points where it intersects as B1 and B2.
- Triangle B1B2A is also a right-angled triangle with legs of length 1 and hypotenuse of length √2. Hence, the area of this triangle is also 0.5 square units.

* Point C: The rubber band intersects with two squares at point C. Let's call the points where it intersects as C1 and C2.
- Triangle C1C2B is yet another right-angled triangle with legs of length 1 and hypotenuse of length √2. Therefore, the area of this triangle is 0.5 square units as well.

**Calculating the Final Area:**
To find the area enclosed by the rubber band, we need to subtract the areas of the overlapping regions from the total area of the squares.

Total area of squares = 1 + 1 + 1 = 3 square units
Area of overlapping regions = 0.5 + 0.5 + 0.5 = 1.5 square units

Final area enclosed by the rubber band = Total area of squares - Area of overlapping regions
= 3 - 1.5
= 1.5 square units

**Conclusion:**
The area enclosed by the rubber band around the squares drawn on the sides of the equilateral triangle is 1.5 square units.

Trapezium