📝 Practice Worksheets
🛠️ Related Tools
🔑 Key Concepts
- The surface area of a prism is the sum of the areas of all of its faces.
- For a triangular prism, surface area can be found with \(SA=ab+Ph\).
- In the formula \(SA=ab+Ph\), \(ab\) represents the total area of the two congruent triangular bases.
- The expression \(Ph\) represents the lateral area from the three rectangular faces.
- The perimeter \(P\) must come from the triangular base, not from the entire outside drawing.
- If the triangular base is isosceles, use that fact to identify repeated side lengths when finding perimeter.
✏️ Worked Examples
💡 Main Idea
To find the surface area of a triangular prism, add the area of the two triangular bases and the area of the three rectangular lateral faces. A helpful shortcut formula is \(SA=ab+Ph\), where \(a\) is the altitude of a triangular base, \(b\) is the base of that triangle, \(P\) is the perimeter of the triangular base, and \(h\) is the height of the prism. In this lesson, students use the dimensions of an isosceles triangular base to find both the area of the bases and the lateral area before combining them for the total surface area.
📚 What You Should Already Know
Before working on this lesson, students should already know how to find the area of a triangle using \(A=\frac{1}{2}bh\), how to find the perimeter of a triangle, and how to identify the height of a prism. Students should also understand that surface area measures the total area covering the outside of a three-dimensional figure.
🚀 What Comes Next
After finding the surface area of triangular prisms, students can extend this work to other prisms, cylinders, pyramids, cones, and composite solids. They will also continue connecting nets, formulas, and three-dimensional figures so they can choose efficient strategies for different surface area problems.
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