Triangular Prism Surface Area Calculator

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Triangular Prism Surface Area Calculator

Enter dimensions and click 'Calculate' to see the surface area.
function calculateSurfaceArea() { var triangleSideA = parseFloat(document.getElementById("triangleSideA").value); var triangleSideB = parseFloat(document.getElementById("triangleSideB").value); var triangleSideC = parseFloat(document.getElementById("triangleSideC").value); var prismLength = parseFloat(document.getElementById("prismLength").value); var resultDiv = document.getElementById("result"); if (isNaN(triangleSideA) || isNaN(triangleSideB) || isNaN(triangleSideC) || isNaN(prismLength) || triangleSideA <= 0 || triangleSideB <= 0 || triangleSideC <= 0 || prismLength <= 0) { resultDiv.innerHTML = "Please enter valid, positive numbers for all dimensions."; return; } // Check triangle inequality theorem if (!((triangleSideA + triangleSideB > triangleSideC) && (triangleSideA + triangleSideC > triangleSideB) && (triangleSideB + triangleSideC > triangleSideA))) { resultDiv.innerHTML = "The given side lengths do not form a valid triangle. The sum of any two sides must be greater than the third side."; return; } // Calculate semi-perimeter of the triangular base var semiPerimeter = (triangleSideA + triangleSideB + triangleSideC) / 2; // Calculate area of the triangular base using Heron's formula var areaBase = Math.sqrt(semiPerimeter * (semiPerimeter – triangleSideA) * (semiPerimeter – triangleSideB) * (semiPerimeter – triangleSideC)); // Calculate perimeter of the triangular base var perimeterBase = triangleSideA + triangleSideB + triangleSideC; // Calculate lateral surface area (sum of the areas of the three rectangular faces) var lateralSurfaceArea = perimeterBase * prismLength; // Calculate total surface area (2 * base area + lateral surface area) var totalSurfaceArea = (2 * areaBase) + lateralSurfaceArea; resultDiv.innerHTML = "

Calculation Results:

" + "Area of Triangular Base: " + areaBase.toFixed(2) + " square units" + "Perimeter of Triangular Base: " + perimeterBase.toFixed(2) + " units" + "Lateral Surface Area: " + lateralSurfaceArea.toFixed(2) + " square units" + "Total Surface Area: " + totalSurfaceArea.toFixed(2) + " square units"; }

Understanding the Triangular Prism Surface Area

A triangular prism is a three-dimensional solid shape that has two identical triangular bases and three rectangular sides. Imagine a slice of cheese shaped like a triangle, and then imagine many such slices stacked up – that's a triangular prism! Understanding its surface area is crucial in various fields, from packaging design to architecture and engineering.

What is Surface Area?

The surface area of any three-dimensional object is the total area of all its faces. For a triangular prism, this means summing the areas of its two triangular bases and its three rectangular lateral faces.

Components of a Triangular Prism's Surface Area

To calculate the total surface area (TSA) of a triangular prism, we need to consider two main parts:

  1. Area of the Two Triangular Bases: Since a prism has two identical bases, we calculate the area of one triangular base and multiply it by two. If the side lengths of the triangle are 'a', 'b', and 'c', we can use Heron's formula to find its area. First, calculate the semi-perimeter (s) of the triangle: s = (a + b + c) / 2. Then, the area of one base (A_base) is √(s * (s - a) * (s - b) * (s - c)).
  2. Area of the Three Rectangular Lateral Faces: These are the sides connecting the two triangular bases. Each rectangular face has a width equal to one of the triangle's sides (a, b, or c) and a length equal to the prism's length (L). So, the area of these three faces combined (Lateral Surface Area, LSA) is (a * L) + (b * L) + (c * L), which simplifies to (a + b + c) * L. Notice that (a + b + c) is simply the perimeter of the triangular base.

Therefore, the total surface area (TSA) of a triangular prism is given by the formula:

TSA = (2 × Area of Triangular Base) + (Perimeter of Triangular Base × Length of Prism)

How to Use the Calculator

Our Triangular Prism Surface Area Calculator simplifies this process for you. Just follow these steps:

  1. Enter Side A, B, and C of Triangular Base: Input the lengths of the three sides of one of the triangular bases. Ensure these values can form a valid triangle (the sum of any two sides must be greater than the third side).
  2. Enter Length of Prism: Input the length or height of the prism, which is the distance between the two triangular bases.
  3. Click "Calculate Surface Area": The calculator will instantly compute and display the area of the triangular base, the lateral surface area, and the total surface area of the prism.

Example Calculation

Let's calculate the surface area for a triangular prism with the following dimensions:

  • Side A of Triangular Base = 3 units
  • Side B of Triangular Base = 4 units
  • Side C of Triangular Base = 5 units
  • Length of Prism = 10 units

Here's how the calculation works:

  1. Perimeter of Triangular Base: 3 + 4 + 5 = 12 units
  2. Semi-perimeter (s): 12 / 2 = 6 units
  3. Area of Triangular Base (using Heron's formula):
    √(6 * (6 - 3) * (6 - 4) * (6 - 5))
    √(6 * 3 * 2 * 1) = √36 = 6 square units
  4. Lateral Surface Area: Perimeter of Base × Length of Prism = 12 × 10 = 120 square units
  5. Total Surface Area: (2 × Area of Base) + Lateral Surface Area = (2 × 6) + 120 = 12 + 120 = 132 square units

Using the calculator with these values will yield a total surface area of 132.00 square units.

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