How To Find The Surface Area Of A Hexahedron

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.