A circle is inscribed in a square with a side length of 12 cm. What is the area of the region outside the circle but inside the square?

Fri, 17 Apr 2026 05:56:10 +0000

**Discover the Hidden Math Behind a Classic Inscription – Area You Can Visualize** Curious about how simple geometry shapes our daily world? A circle inscribed in a square with a 12 cm side length offers a captivating blend of precision and real-world application. This common shape problem isn’t just for classrooms—it’s gaining attention in digital spaces where users explore patterns, design, and spatial reasoning. Understanding its area reveals more than just numbers; it uncovers principles behind design, efficiency, and spatial relationships widely used in architecture, product design, and visual art. A circle inscribed in a square touches all four sides exactly at their midpoints, meaning its diameter matches the square’s side length. With the square measuring 12 cm across, the inscribed circle has a diameter of 12 cm—and thus a radius of 6 cm. From this, we calculate the area of both the square and the circle to reveal the blank region between them. The square’s total area is 12 × 12 = 144 cm². The circle’s area, using the formula πr², is π × 6² = 36π cm². Subtracting 36π from 144 gives the area outside the circle but inside the square—about 144 – 113.1 = 30.9 cm², depending on π’s approximation. This calculation highlights how even simple shapes form measurable, meaningful space—ideal for learning spatial literacy and confidence in personal and professional decision-making.