Question: A triangular prism has a base that is a right triangle with legs $ 5 $ and $ 12 $, and a height of $ 10 $. What is the length of the longest edge of the prism?

Mon, 20 Apr 2026 01:23:39 +0000

**Why the Triangular Prism with Right Triangle Base Fascinates Designers & Educators in 2025** In the modern landscape of geometry, teaching tools that blend visual intuition with mathematical precision are in high demand. The triangular prism—especially one rooted in a right triangle base with legs 5 and 12 and height 10—has emerged as a favored topic in classrooms and online learning communities. With its organic symmetry and measurable complexity, it sparks interest in applied geometry, architectural design, and even structural engineering. As digital learning tools grow, this shape isn’t just a classroom example—it’s a gateway to understanding real-world 3D forms and their practical roles. **Why This Prism is Gaining Attention Across the US** Recent trends in STEM education emphasize hands-on, visual learning, and the triangular prism stands out as a compelling subject. Its design—sharp edges, defined angles, and measurable height—makes it ideal for exploring spatial reasoning and volume calculations. Educators and content creators note rising interest from students, parents seeking educational resources, and tech-informed curricula focusing on intuitive geometry. As curiosity around STEM deepens, this prism exemplifies how abstract shapes connect to tangible learning outcomes. **What Defines the Longest Edge of the Prism?** To uncover the longest edge, break down the prism’s structure: the base is a right triangle with side lengths 5 and 12; the height—also known as the prism height—is perpendicular to this triangular base and extends the full length of the prism. The key is understanding both the triangle’s hypotenuse and the vertical height’s full span. While the triangle’s hypotenuse measures 13 via the Pythagorean theorem, the prism’s longest edge extends the full height of 10 units through space—creating a diagonal vector across the shape’s depth and height. **Breaking Down the Geometry: The Longest Edge Revealed** The triangular base yields a hypotenuse of length 13 using \( \sqrt{5^2 + 12