Volume and Surface Area of Prisms

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.

SA=6s^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=Ph+2B 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=4s 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.

SA= P h+2 B
SA= 4s( s)+2 s^2
SA=4s^2+2s^2
SA=6s^2

Exercises
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