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Given an equilateral triangle of side 1 , squares are drawn on all the three sides. if a rubber band stretches around the squares , the area of the region enclosed by the rubber band is ?
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Given an equilateral triangle of side 1 , squares are drawn on all the...
**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.
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Given an equilateral triangle of side 1 , squares are drawn on all the...
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Given an equilateral triangle of side 1 , squares are drawn on all the three sides. if a rubber band stretches around the squares , the area of the region enclosed by the rubber band is ?
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Given an equilateral triangle of side 1 , squares are drawn on all the three sides. if a rubber band stretches around the squares , the area of the region enclosed by the rubber band is ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Given an equilateral triangle of side 1 , squares are drawn on all the three sides. if a rubber band stretches around the squares , the area of the region enclosed by the rubber band is ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given an equilateral triangle of side 1 , squares are drawn on all the three sides. if a rubber band stretches around the squares , the area of the region enclosed by the rubber band is ?.
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