Calculate Face Area of Cube with 42 cm² Surface Area: Visual Geometry Problem

To solve this problem, we'll follow these steps:

• Step 1: Use the formula for the surface area of a cube: $S = 6s^2$.
• Step 2: Plug in the given total surface area into the formula to find $s^2$.
• Step 3: Calculate the area of one face of the cube.

Now, let's work through each step:
Step 1: We are given that the total surface area $S$ is 42 cm².
Step 2: Substitute the given surface area into the formula: $6s^2 = 42$
To find $s^2$, divide both sides of the equation by 6: $s^2 = \frac{42}{6} = 7$
Step 3: The area of one face of the cube equals $s^2$, so the area of one face is 7 cm².

Therefore, the area of the face highlighted is $7 \, \text{cm}^2$.