A square has a diagonal measuring 10√2 cm. What is the area of the square?
["# A Square Has a Diagonal Measuring (10\sqrt{2}) cm — What Is the Area of the Square?", "Understanding the relationship between a square’s diagonal and its area can be simpler than you might expect. In this article, we’ll explore how to determine the area of a square when given the length of its diagonal — specifically, when the diagonal measures (10\sqrt{2}) cm.", "## Why Diagonal Matters in a Square", "A square is a special type of quadrilateral where all sides are equal, and all angles are right angles. One key property is that the diagonals of a square are equal in length, bisect each other at 90 degrees, and divide the square into two congruent right-angled triangles.", "The diagonal acts as the hypotenuse of these right triangles, connecting two opposite corners of the square. This geometric relationship allows us to calculate side length and area using the diagonal.", "## How to Find the Side Length from the Diagonal", "Let (s) be the length of one side of the square. From geometry, we know that in a square, the diagonal (d) relates to the side length via the Pythagorean theorem:", "[\nd = s\sqrt{2}\n]", "Given:\n[\nd = 10\sqrt{2} \ ext{ cm}\n]", "Substitute into the formula:\n[\n10\sqrt{2} = s\sqrt{2}\n]", "Divide both sides by (\sqrt{2}):\n[\ns = 10 \ ext{ cm}\n]", "So, each side of the square is 10 cm.", "## Calculating the Area", "The area (A) of a square is simply the square of its side length:\n[\nA = s^2 = 10^2 = 100 \ ext{ cm}^2\n]", "## Summary", "When a square has a diagonal measuring (10\sqrt{2}) cm, its area is 100 square centimeters.", "- Diagonal: (10\sqrt{2}) cm\n- Side length: 10 cm\n- Area: (100 \ ext{ cm}^2)", "Understanding this relationship helps solve geometry problems efficiently — especially when working with squares and their diagonal measurements. Whether you're studying for exams, designing architectural plans, or solving real-world measurement challenges, knowing how to calculate area from the diagonal saves time and reduces errors.", "---", "Keywords: square area, diagonal of square, geometry, square diagonal calculation, area of a square formula, (10\sqrt{2}) cm diagonal, math problem solving, geometry education", "Meta description: Learn how to find the area of a square with a diagonal of (10\sqrt{2}) cm using geometry principles—side length 10 cm, area 100 cm². Perfect for math students and educators."]
