This means we have to calculate the area of each rectangle. So, the area of the base and top is twice the base area. So, we can say that the total surface area of both the top and base of the prism isĪ B = b a s e a r e a A T = t o p a r e a A T B = A r e a o f b a s e a n d t o p A B = A T A T B = A B + A T A T B = A B + A B A T B = 2 A B The area of the top must surely be the same as the base area which depends on the shape of the base. We have 2 identical sides which take the shape of the prism, and n rectangular sides - where n is the number of sides of the base. Now that we know what the surfaces of a prism comprise, it is easier to calculate the total surface area of a prism. Likewise, a pentagonal base prism will have 5 other sides apart from its identical top and base, and this applies to all prisms.Īn illustration of the rectangular faces of a prism using a triangular prism, StudySmarter OriginalsĪlways remember that the sides which are different from the top and base are rectangular - this will help you in understanding the approach used in developing the formula. For instance, a triangular base prism will have 3 other sides aside from its identical top and base. It also comprises rectangular surfaces depending on the number of sides the prism base has. Triangular PrismĪ triangular prism has 5 faces including 2 triangular faces and 3 rectangular ones.Īn image of a triangular prism, StudySmarter Originals Rectangular PrismĪ rectangular prism has 6 faces, all of which are rectangular.Īn image of a rectangular prism, StudySmarter Originals Pentagonal PrismĪ pentagonal prism has 7 faces including 2 pentagonal faces and 5 rectangular faces.Īn image of a pentagonal prism, StudySmarter Originals Trapezoidal PrismĪ trapezoidal prism has 6 faces including 2 trapezoidal faces and 4 rectangular ones.Īn image of a trapezoidal prism, StudySmarter Originals Hexagonal PrismĪ hexagonal prism has 8 faces including 2 hexagonal faces and 6 rectangular faces.Īn image of a hexagonal prism, StudySmarter Originals In general, it can be said that all polygons can become prisms in 3D and hence their total surface areas can be calculated. There are many different types of prisms that obey the rules and formula mentioned above. 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.The total surface area of a prism is the sum of twice its base area and the product of the perimeter of the base and the height of the prism. 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. 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. 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. 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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