A rectangle has a diagonal of 13 cm and one side 5 cm. What is the area of the rectangle?

Thu, 30 Apr 2026 04:01:24 +0000

**A rectangle has a diagonal of 13 cm and one side 5 cm. What is the area of the rectangle?** Why this rectangle is trending in U.S. digital spaces
Understanding geometric relationships—like diagonal length and side measurements—remains a quiet favorite in STEM communities and everyday tech discussions. Social media feeds, educational videos, and online problem-solving forums increasingly spotlight real-life math puzzles like this. What makes a rectangle with a 13 cm diagonal and one 5 cm side particularly engaging is its clean simplicity combined with the satisfying challenge of finding hidden dimensions and area. This query reflects rising curiosity about practical geometry—how theoretical shapes connect to real-world design, construction, and app-based tutorials. Whether navigating interior planning, fitness tracking, or digital design tools, simple rectangles with known diagonals are surprisingly relevant. **Why a rectangle with a 13 cm diagonal and one 5 cm side matters**
This specific geometric problem taps into a common pattern: given a diagonal and one side, derive total area. In the U.S., where mobile learning and quick-tech tutorials dominate mobile search behavior, problems like this serve as accessible entry points to deeper mathematical reasoning. They’re shared across parenting, education, and producer communities—not just math enthusiasts. The diagonal acts as a focal reference point, linking side lengths to area through the Pythagorean theorem. As users explore how dimensions contribute to space, rectangle geometry evolves from abstract concept to practical tool for decision-making. **How to find the area of a rectangle with a diagonal of 13 cm and one side 5 cm**
Start by applying the Pythagorean theorem, a foundational principle linking the sides and the diagonal. For a rectangle, the diagonal splits into two right triangles, each with legs equal to the side lengths and hypotenuse the diagonal. With one side (let’s call it *a*) measuring 5 cm and diagonal (*c*) 13 cm, we calculate the missing side (*b*) using:
c² = a² + b²
13² = 5² + b²
169 = 25 + b²
b² = 144
b = 12 cm