Finding the surface area of a hexahedron, also known as a cube, involves using the length of its sides. This guide will provide a step-by-step process to determine the surface area using a specific formula.
Step 1: Show the Surface Area Formula
The formula for the surface area \(SA\) of a hexahedron is:
\[ SA = 6 \cdot a^2 \]
Where:
- \(a\) is the length of each side of the cube.
Step 2: Explain the Formula
In this formula:
- \(6 \cdot a^2\) represents the total surface area of the six square faces of the hexahedron. Each face has an area of \(a^2\), and since a cube has six faces, the total surface area is \(6 \cdot a^2\).
Step 3: Insert Numbers as an Example
Let's consider a hexahedron with a side length \(a = 4\) units.
Step 4: Calculate the Final Value
First, we substitute the value into the formula:
\[ SA = 6 \cdot 4^2 \]
Next, we calculate the square of the side length:
\[ SA = 6 \cdot 16 \]
Now, multiply the numbers:
\[ SA = 96 \, \text{square units} \]
Final Value
The surface area of a hexahedron with a side length of 4 units is 96 square units.
