How to Calculate the Surface Area of a Triangular Prism

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Triangular Prism Surface Area Calculator

Calculate the total surface area of any triangular prism quickly and accurately.

Calculation Results

Base Area (per triangle): 0
Lateral Surface Area: 0
Total Surface Area: 0

How to Calculate the Surface Area of a Triangular Prism

A triangular prism is a three-dimensional polyhedron made up of two triangular bases and three rectangular lateral faces. To find the total surface area, you must calculate the area of all five faces and sum them together.

The Surface Area Formula

The standard formula for the surface area of a triangular prism is:

Surface Area = (Perimeter of base × Length of prism) + (2 × Area of base)

Step-by-Step Breakdown

  1. Find the Area of the Triangular Base: Using the base (b) and vertical height (h) of the triangle, use the formula Area = 0.5 × b × h. Since there are two identical bases, multiply this by 2.
  2. Find the Perimeter of the Base: Add the lengths of the three sides of the triangular base (a + b + c).
  3. Calculate the Lateral Area: Multiply the perimeter of the base by the length (L) of the prism. This accounts for the three rectangular sides.
  4. Add them together: Sum the area of the two bases and the lateral area to get your total surface area.

Practical Example

Imagine a triangular prism with the following dimensions:

  • Triangle Sides: 3 cm, 4 cm, and 5 cm (a right-angled triangle)
  • Triangle Height: 4 cm
  • Prism Length: 10 cm

Step 1: Base Area
Area = 0.5 × 3 × 4 = 6 cm². Two bases = 12 cm².

Step 2: Perimeter
Perimeter = 3 + 4 + 5 = 12 cm.

Step 3: Lateral Area
Lateral Area = 12 × 10 = 120 cm².

Step 4: Total Surface Area
Total = 12 + 120 = 132 cm².

Why is this important?

Calculating the surface area of a triangular prism is essential in fields like architecture, packaging design (like Toblerone boxes!), and construction. It helps determine the amount of material needed to wrap, paint, or manufacture a 3D object.

function calculateTriPrismArea() { var a = parseFloat(document.getElementById('sideA').value); var b = parseFloat(document.getElementById('sideB').value); var c = parseFloat(document.getElementById('sideC').value); var h = parseFloat(document.getElementById('triHeight').value); var L = parseFloat(document.getElementById('prismLength').value); if (isNaN(a) || isNaN(b) || isNaN(c) || isNaN(h) || isNaN(L) || a <= 0 || b <= 0 || c <= 0 || h <= 0 || L <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Area of one triangular base // Note: sideA is used as the base for the height h var baseArea = 0.5 * a * h; // Perimeter of the triangle var perimeter = a + b + c; // Lateral surface area (the 3 rectangles) var lateralArea = perimeter * L; // Total Surface Area = (2 * baseArea) + lateralArea var totalArea = (2 * baseArea) + lateralArea; // Display Results document.getElementById('resBaseArea').innerText = baseArea.toFixed(2) + " sq units"; document.getElementById('resLateralArea').innerText = lateralArea.toFixed(2) + " sq units"; document.getElementById('resTotalArea').innerText = totalArea.toFixed(2) + " sq units"; document.getElementById('results-box').style.display = 'block'; }

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