Total Surface Area Of Cuboid Given Perimeter, Height, And Width Calculator

Formula Used:

\[ \text{Total Surface Area} = 2 \times \left( \text{Width} \times \text{Height} + \text{Height} \times \text{Length} + \text{Width} \times \text{Length} \right) \] \[ \text{Length} = \frac{\text{Perimeter} - 4 \times (\text{Width} + \text{Height})}{4} \]

Total Surface Area:

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1. What is Total Surface Area of Cuboid?

The total surface area of a cuboid is the sum of the areas of all six rectangular faces. It represents the complete external surface area of the three-dimensional rectangular prism.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ \text{Length} = \frac{\text{Perimeter} - 4 \times (\text{Width} + \text{Height})}{4} \] \[ \text{Total Surface Area} = 2 \times (\text{Width} \times \text{Height} + \text{Height} \times \text{Length} + \text{Width} \times \text{Length}) \]

Where:

Perimeter - Total perimeter of the cuboid
Height - Vertical dimension of the cuboid
Width - Horizontal dimension of the cuboid
Length - Calculated dimension from perimeter, height and width

Explanation: The calculator first derives the length from the given perimeter, height and width, then calculates the total surface area using the standard cuboid surface area formula.

3. Importance of Surface Area Calculation

Details: Surface area calculations are crucial in various fields including construction, packaging, manufacturing, and material estimation. It helps determine the amount of material needed to cover a three-dimensional object.

4. Using the Calculator

Tips: Enter the perimeter, height, and width in consistent units. All values must be positive numbers. The calculator will automatically compute the length and total surface area.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between total surface area and lateral surface area?
A: Total surface area includes all six faces, while lateral surface area only includes the four side faces (excluding top and bottom).

Q2: Can this calculator handle different units?
A: The calculator works with any consistent unit system (cm, m, inches, etc.) as long as all inputs use the same unit.

Q3: What if the calculated length becomes negative?
A: A negative length indicates invalid input values where the given perimeter cannot accommodate the specified height and width dimensions.

Q4: How accurate are the results?
A: Results are accurate to two decimal places, providing precise calculations for practical applications.

Q5: Can this be used for cubes?
A: Yes, when all dimensions are equal (length = width = height), the calculator will provide correct surface area for cubes as well.