Today, the surface area of a triangular prism remains a fundamental principle in geometry and continues to serve as a crucial element in a multitude of practical applications. ![]() It is determined with the formula: Surface area bh + L (s1 + s2 + s3) where, b is the bottom edge of the base triangle, h is the height of the base triangle, s 1, s 2, and s 3 are the sides of the triangular bases. Their studies on triangles, parallelograms, and three-dimensional shapes have greatly influenced contemporary understanding of geometry and the surface area of various shapes, including triangular prisms. Surface area of a triangular prism is the sum of the areas of all the faces of the prism. While there is no definitive historical account of the origin of the triangular prism or its surface area concept, it can be traced back to ancient Greece, where mathematicians like Euclid and Pythagoras laid the groundwork for modern geometry. Moreover, artists and designers frequently employ triangular prisms in their creations, making the knowledge of surface area invaluable for conceptualizing and executing their work. In packaging design, calculating the surface area of a triangular prism helps optimize material usage, reduce waste, and minimize costs. For instance, in construction and architecture, the surface area plays a role in determining the stability and strength of structures, as well as insulation and energy efficiency. Triangular prisms, like other three-dimensional shapes, have numerous real-life applications that make understanding their surface area essential. Step 1: Determine the base area and the height of the prism. The concept of surface area has broad applications in various fields, including engineering, architecture, and design, where it is crucial to estimate material requirements, costs, and structural integrity. Solved example Example: Calculate the surface area of a triangular prism with side 7 cm, base 5 cm and height 6 cm. ![]() ![]() A triangular prism consists of two congruent triangles at the ends, known as bases, connected by three parallelogram-shaped lateral faces. The surface area of a triangular prism is a key concept in geometry that pertains to the total area covering the external faces of the three-dimensional shape.
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