Total Surface Area of Cuboid given Perimeter, Length, and Width Calculator

Formula Used:

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

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 total area that the surface of the cuboid occupies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Total Surface Area} = 2 \times (L \times W + L \times H + W \times H) \] \[ H = \frac{P - 4 \times (L + W)}{4} \]

Where:

\( L \) — Length of the cuboid
\( W \) — Width of the cuboid
\( H \) — Height of the cuboid
\( P \) — Perimeter of the cuboid

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

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, packaging design, heat transfer calculations, and construction planning.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a cuboid?
A: A cuboid is a three-dimensional shape with six rectangular faces, where all angles are right angles and opposite faces are equal.

Q2: How is perimeter related to cuboid dimensions?
A: The perimeter of a cuboid refers to the sum of all edges. For a cuboid, perimeter = 4 × (length + width + height).

Q3: What units should I use?
A: Use consistent units for all measurements (e.g., all in meters, centimeters, or inches). The result will be in square units of the input.

Q4: Can this calculator handle decimal values?
A: Yes, the calculator accepts decimal values for more precise calculations.

Q5: What if I get a negative height value?
A: A negative height indicates that the input values are inconsistent with a valid cuboid. Please check your perimeter, length, and width values.