Surface Area Of A Triangular Prisms

🔑 Key Concepts

  • A triangular prism has 2 congruent triangular bases and 3 rectangular lateral faces.
  • The surface area can be found by adding the areas of all 5 faces.
  • The formula \(SA=ab+Ph\) combines the two triangular bases and the three rectangles.
  • In \(SA=ab+Ph\), \(a\) is the altitude of the triangular base, \(b\) is the base of the triangle, \(P\) is the perimeter of the triangular base, and \(h\) is the height or length of the prism.
  • Surface area is measured in square units.

✏️ Worked Examples

🧠 Math Vocabulary

  • Triangular Prism: a three-dimensional figure with 2 congruent triangular bases and 3 rectangular lateral faces.
  • Prism: a three-dimensional figure with two congruent, parallel bases connected by rectangular faces.
  • Surface Area: the total area of all outside faces of a three-dimensional figure.
  • Congruent Faces: faces that have the same size and shape.
  • Triangular Bases: the two congruent triangle faces of a triangular prism.
  • Lateral Faces: the rectangular faces that connect the two triangular bases.
  • Altitude: the perpendicular height of the triangular base.
  • Perimeter: the distance around the triangular base.
  • Net: a two-dimensional pattern that can fold into a three-dimensional figure.
  • Square Units: units used to measure area, such as \(\text{in}^2\), \(\text{cm}^2\), or \(\text{units}^2\).

💡 Main Idea

To find the surface area of a triangular prism, add the areas of the two congruent triangular bases and the three rectangular lateral faces. The formula \(SA=ab+Ph\) combines those same parts into one expression.

📚 What You Should Already Know

Students should already know how to find the area of triangles and rectangles, identify congruent faces, calculate perimeter, and understand that surface area measures the outside covering of a three-dimensional figure.

🚀 What Comes Next

Students can extend these ideas to other prisms, cylinders, pyramids, cones, and composite three-dimensional figures.

🧩 Embed This Video in Your LMS

Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.