Hello!
Let’s begin by finding the surface area of one of the cube’s six faces. The formula for the surface area of a square can be written as follows:
area = length × width
We are given that the length, width, and height of the cube in the image above all have a length of 7mm. Now we’ll insert any relevant values into the formula above:
area = (7mm) × (7mm)
Simplify the right side of the equation:
area = 49mm²
We have now proven that the surface area of one face is equal to 49mm². However, we are asked to find the total surface area of the given cube. Because a cube has six identical faces, we can use the proven area of one face to find the total surface area of the cube. We’ll begin with the following formula:
total surface area = (area of face #1) × 6
Now insert the proven value of the first face:
total surface area = (49mm²) × 6
Simplify the right side of the equation:
total surface area = 294mm²
We have now proven that the total surface area of the given cube is 294mm².
I hope this helps!