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Lateral Surface Area Of Icosahedron Given Total Surface Area Calculator

Formula Used:

\[ LSA = \frac{9}{10} \times TSA \]

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1. What is the Lateral Surface Area of Icosahedron?

The Lateral Surface Area of an Icosahedron is the quantity of plane enclosed by all the lateral surfaces (excluding the top and bottom faces) of the Icosahedron. It represents the surface area of all the side faces combined.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ LSA = \frac{9}{10} \times TSA \]

Where:

Explanation: This formula calculates the lateral surface area as 90% of the total surface area, since the lateral surface area excludes the top and bottom faces of the icosahedron.

3. Importance of Lateral Surface Area Calculation

Details: Calculating the lateral surface area is important in various geometric and engineering applications where only the side surfaces need to be considered, such as in material estimation for construction or manufacturing processes.

4. Using the Calculator

Tips: Enter the total surface area of the icosahedron in square meters. The value must be a positive number greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is an Icosahedron?
A: An icosahedron is a polyhedron with 20 faces, 30 edges, and 12 vertices. It is one of the five Platonic solids.

Q2: Why is the lateral surface area 9/10 of the total surface area?
A: This ratio accounts for the exclusion of specific faces (typically considered as top and bottom) from the total surface area calculation.

Q3: Can this formula be used for all types of icosahedrons?
A: This formula applies specifically to regular icosahedrons where all faces are equilateral triangles and the shape is symmetrical.

Q4: What are the units for lateral surface area?
A: The lateral surface area is measured in square units (m², cm², etc.), matching the units of the input total surface area.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular icosahedrons when the input values are accurate.

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