Calculate the total surface area
Step 1: Identify the Triangular Base
Measure base (b), height (h of triangle), and the two other sides (a, c) of the triangle.
Why: The triangular faces are critical to surface area; you need all three sides for the perimeter.
Step 2: Measure Prism Length
Find L, the distance between the two triangular faces (depth of the prism).
Why: Prism length scales the three rectangular faces; missing it prevents calculation.
Step 3: Calculate Triangular Base Area
Use A_triangle = (1/2) × base × height.
Why: The prism has two identical triangular faces (top and bottom); calculating area once and doubling is efficient.
Step 4: Calculate Perimeter of Triangle
Perimeter = a + base + c (sum of all three triangle sides).
Why: The three rectangular faces have widths equal to each side of the triangle.
Step 5: Total Surface Area
SA = (Perimeter × L) + (2 × Triangle Area). This accounts for three rectangular faces plus two triangular faces.
Why: A triangular prism has 5 total faces: 2 triangles and 3 rectangles.
SA = (a + b + c)L + bh
Where a, b, c are sides of the triangular base, h is the height of the triangle, and L is the length of the prism.
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