Find the Area of the Blue Square: A Geometry Puzzle

Published on September 7, 2024

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.
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