Surface Area of a Triangular Prism Calculator

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Triangular Prism Surface Area Calculator

function calculateSurfaceArea() { var triangleBase = parseFloat(document.getElementById('triangleBase').value); var triangleHeight = parseFloat(document.getElementById('triangleHeight').value); var triangleSide1 = parseFloat(document.getElementById('triangleSide1').value); var triangleSide2 = parseFloat(document.getElementById('triangleSide2').value); var triangleSide3 = parseFloat(document.getElementById('triangleSide3').value); var prismLength = parseFloat(document.getElementById('prismLength').value); if (isNaN(triangleBase) || isNaN(triangleHeight) || isNaN(triangleSide1) || isNaN(triangleSide2) || isNaN(triangleSide3) || isNaN(prismLength) || triangleBase <= 0 || triangleHeight <= 0 || triangleSide1 <= 0 || triangleSide2 <= 0 || triangleSide3 <= 0 || prismLength <= 0) { document.getElementById('result').innerHTML = 'Please enter valid positive numbers for all dimensions.'; return; } // Area of the two triangular bases var areaOfBaseTriangle = 0.5 * triangleBase * triangleHeight; var totalBaseArea = 2 * areaOfBaseTriangle; // Perimeter of the triangular base var perimeterOfBase = triangleSide1 + triangleSide2 + triangleSide3; // Area of the three rectangular sides var lateralSurfaceArea = perimeterOfBase * prismLength; // Total Surface Area var totalSurfaceArea = totalBaseArea + lateralSurfaceArea; document.getElementById('result').innerHTML = 'The total surface area of the triangular prism is: ' + totalSurfaceArea.toFixed(2) + ' square units.'; }

Understanding the Surface Area of a Triangular Prism

A triangular prism is a three-dimensional geometric shape composed of two parallel and congruent triangular bases and three rectangular sides connecting them. Imagine a slice of cheese shaped like a triangle; if you extend that triangle straight up, you get a triangular prism. Calculating its surface area means finding the total area of all its faces combined.

What is Surface Area?

Surface area refers to the total area of the outer surface of a three-dimensional object. For a triangular prism, this includes the area of its two triangular bases and the area of its three rectangular sides.

Formula for Surface Area of a Triangular Prism

The formula to calculate the total surface area (SA) of a triangular prism is:

SA = (2 × Area of Base Triangle) + (Perimeter of Base Triangle × Length of Prism)

Let's break down the components:

  • Area of Base Triangle: This is calculated as 0.5 × base × height_t, where 'base' (b) is the length of the base of the triangle and 'height_t' (h_t) is the altitude (perpendicular height) of the triangle. Since there are two identical triangular bases, we multiply this area by 2.
  • Perimeter of Base Triangle: This is the sum of the lengths of the three sides of the triangular base (s1 + s2 + s3).
  • Length of Prism (L): This is the distance between the two triangular bases, often referred to as the height of the prism.

Combining these, the formula can also be written as:

SA = (b × h_t) + ((s1 + s2 + s3) × L)

How to Use the Calculator

Our calculator simplifies this process. You'll need to input the following dimensions:

  1. Base of Triangle (b): The length of one side of the triangular base.
  2. Height of Triangle (h_t): The perpendicular height from the base to the opposite vertex of the triangle.
  3. Side 1, Side 2, Side 3 of Triangle (s1, s2, s3): The lengths of all three sides of the triangular base. These are needed to calculate the perimeter.
  4. Length of Prism (L): The distance between the two triangular bases.

Once you enter these values, click "Calculate Surface Area," and the total surface area will be displayed.

Example Calculation

Let's consider a triangular prism with the following dimensions:

  • Base of Triangle (b) = 6 cm
  • Height of Triangle (h_t) = 4 cm
  • Sides of Triangle (s1, s2, s3) = 5 cm, 5 cm, 6 cm (an isosceles triangle)
  • Length of Prism (L) = 10 cm

Using the formula:

  1. Area of one base triangle: 0.5 × 6 cm × 4 cm = 12 cm²
  2. Total area of two bases: 2 × 12 cm² = 24 cm²
  3. Perimeter of base triangle: 5 cm + 5 cm + 6 cm = 16 cm
  4. Lateral surface area (three rectangular sides): 16 cm × 10 cm = 160 cm²
  5. Total Surface Area: 24 cm² + 160 cm² = 184 cm²

So, the surface area of this triangular prism is 184 square centimeters.

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