body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Rule

Surface Area of a Cube

Consider a cube with a side length

s .

The surface area of the cube is given by the following formula.

$S A = 6 s^{2}$

Proof

The surface area of a prism is the sum of the lateral area and the combined areas of the two identical bases.

S = P h + 2 B

Since the base of a cube is a square with a side length

s,

its area is equal to the square of

s .

B = s^{2}

The perimeter of the square base can be calculated as the product of

4

and

s .

P = 4 s

Finally, the height of the cube is also equal to the side length

s .

h = s

Now these values will be substituted into the formula and the resulting equation simplified.

S A = P h + 2 B

SubstituteValues

Substitute values

S A = 4 s (s) + 2 s^{2}

ProdToPowTwoFac

$a \cdot a = a^{2}$

S A = 4 s^{2} + 2 s^{2}

AddTerms

Add terms

S A = 6 s^{2}

Exercises

Recommended exercises

To get personalized recommended exercises, please login first.

Return to lesson.