Calculators / Geometry / Surface Area of a Triangular Prism Calculator

Surface Area of a Triangular Prism Calculator

Published on: July 28, 2024

This Surface Area of a Triangular Prism Calculator helps you find the total area of all faces of a right triangular prism when the triangle base, triangle height, and prism length are known. It uses the areas of the two triangular ends and the three rectangular faces to find the total surface area, and the answer is written in square units. First find the area of the triangular base and the lengths needed for the side faces, then add all face areas together. It is a simple way to check answers, understand the triangular prism surface area formula, and practise basic geometry step by step.
Triangular prism labeled b, h, ℓ
The triangle has legs b and h, and the prism extends by ℓ.

Step-by-step method

  1. Identify what is given.
  2. Write the surface area formula.
  3. Find the triangle’s hypotenuse.
  4. Substitute the values and calculate the surface area.

Formula:

A = (b + h + √(b² + h²))ℓ + b·h

Example 1: b = 3.50, h = 4.20, ℓ = 5.10

Step 1 - Identify what is given.

In this problem: The given values are b = 3.50, h = 4.20, ℓ = 5.10.

b=3.50,h=4.20,ℓ=5.10

Step 2 - Write the surface area formula.

In this problem: Use the surface area formula for a right triangular prism: A = (b + h + √(b² + h²))ℓ + b·h.

A=(b + h + √(b² + h²))ℓ + b·h

Step 3 - Find the triangle’s hypotenuse.

In this problem: Find the hypotenuse: c = √(b² + h²) = √(3.50² + 4.20²) = 5.47.

c=√(3.50² + 4.20²)=5.47

Step 4 - Substitute the values and calculate the surface area.

In this problem: Substitute b = 3.50, h = 4.20, ℓ = 5.10, c = 5.47: A = (3.50 + 4.20 + 5.47)×5.10 + 3.50×4.20 = 81.85.

A=(3.50 + 4.20 + 5.47)×5.10 + 3.50×4.20=81.85

Final answer: A = 81.85

Example 2: b = 6.25, h = 2.50, ℓ = 4.75

Step 1 - Identify what is given.

In this problem: The given values are b = 6.25, h = 2.50, ℓ = 4.75.

b=6.25,h=2.50,ℓ=4.75

Step 2 - Write the surface area formula.

In this problem: Use the surface area formula for a right triangular prism: A = (b + h + √(b² + h²))ℓ + b·h.

A=(b + h + √(b² + h²))ℓ + b·h

Step 3 - Find the triangle’s hypotenuse.

In this problem: Find the hypotenuse: c = √(b² + h²) = √(6.25² + 2.50²) = 6.73.

c=√(6.25² + 2.50²)=6.73

Step 4 - Substitute the values and calculate the surface area.

In this problem: Substitute b = 6.25, h = 2.50, ℓ = 4.75, c = 6.73: A = (6.25 + 2.50 + 6.73)×4.75 + 6.25×2.50 = 89.16.

A=(6.25 + 2.50 + 6.73)×4.75 + 6.25×2.50=89.16

Final answer: A = 89.16