Calculate Shaded Area in a Rectangle with Identical Rectangles

Understanding the Geometric Setup

• 💡 The problem features four identical tiny rectangles perfectly confined within a larger blue rectangle.
• 🎯 The objective is to determine the area of a specific green shaded region within this composite figure.

Total Area of the Blue Rectangle

• 🔑 Each of the tiny identical rectangles is assigned an area denoted as 'A'.
• 📈 Consequently, the total area of the big blue rectangle is the sum of these four individual areas, resulting in 4A.

Calculating the White Unshaded Area

• 🔍 The area of the green shaded region can be derived by subtracting the total white unshaded area from the big blue rectangle's area.
• 🧩 Each of the two distinct white unshaded regions is observed to be half the area of a larger rectangle formed by two tiny rectangles (which would be 2A).
• ✅ Therefore, each white region's area is A, making the combined total white unshaded area 2A.

Determining the Green Shaded Area

• 🚀 Applying the principle, the Green Shaded Area = Blue Rectangle Area - White Shaded Area.
• 📊 Substituting the calculated values, the Green Shaded Area = 4A - 2A = 2A.

Final Conclusion

• ✨ The ultimate finding is that the green shaded region's area constitutes half of the big blue rectangle's total area.
• 💡 This implies that the white unshaded region's total area is also half of the blue rectangle's total area.