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Find the Area of the Blue Square: A Geometry Puzzle
Published on September 7, 2024
Geometry
This math problem asks you to find the area of a blue square inside a larger square. The larger square has sides of 4 units, and the blue square is surrounded by four white triangles. By calculating the area of the larger square and subtracting the area of the four triangles, we find the area of the blue square to be 10 square units.
Question
Answer
Let’s break down this problem step-by-step to find the area of the blue square.
1. Visualize the Bigger Picture
- Imagine the blue square is part of a larger square formed by the outer black lines.
2. Calculate the Area of the Larger Square
- The larger square has sides of length (3 + 1) = 4 units.
- The area of a square is side * side, so the larger square’s area is 4 * 4 = 16 square units.
3. Calculate the Area of the Triangles
- Notice the four white triangles surrounding the blue square. Each triangle has:
- A base of 3 units.
- A height of 1 unit.
- The area of a triangle is (1/2) * base * height. So, each triangle’s area is (1/2) * 3 * 1 = 1.5 square units.
4. Subtract to Find the Blue Square’s Area
- The blue square’s area is the larger square’s area minus the area of the four triangles.
- Blue square area = 16 - (1.5 + 1.5 + 1.5 + 1.5) = 16 - 6 = 10 square units.
Answer: The area of the colored square is 10 square units.