To find the surface area of a cube we must count the number of surface faces and add the areas of each of them together.

In a cube there are 6 faces, each a square with the same side lengths.

In this example the side lengths is 15 so the area of each square would be \(\displaystyle 15^2=225\)

We then multiply this number by 6, the number of faces of the cube, to get \(\displaystyle 225*6=1350\)

Our answer for the surface area is \(\displaystyle 1350\).

To find the surface area of a cube, we must count the number of surface faces and add the areas of each together. In a cube there are \(\displaystyle 6\) faces, each a square with the same side lengths. In this example the side length is \(\displaystyle 7\).

The area of a square is given by the equation \(\displaystyle A=s*s=s^2\). Using our side length, we can solve the area of once face of the cube.

\(\displaystyle A=(7)^{2}=49\)

We then multiply this number by \(\displaystyle 6\), the number of faces of the cube to find the total surface area.

\(\displaystyle 49*6=294\)

Our answer for the surface area is \(\displaystyle 294\).

The surface area of a cube = 6a² where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a² → a² = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

In order to find the surface area of a cube, use the formula \(\displaystyle SA=6(s^{2})\).

\(\displaystyle SA=6*(7.2in)^{2}\)

\(\displaystyle SA=6*51.84in^{2}\)

\(\displaystyle SA=311.04in^{2}\)

\(\displaystyle \rightarrow 311in^{2}\)

In order to find the surface area of a rectangular prism, use the formula \(\displaystyle SA=(2*lw)+(2*wh)+(2*lh)\).

However, all units must be the same. All of the units of this problem are in inches with the exception of \(\displaystyle \dpi{100} l=2.2ft\).

Convert to inches.

\(\displaystyle l=\frac{2.2ft}{1}*\frac{12in}{1ft}\)

\(\displaystyle l=26.4in\)

Now, we can insert the known values into the surface area formula in order to calulate the surface area of the rectangular prism.

\(\displaystyle SA=(2*26.4in*18in)+(2*18in*14in)+(2*26.4in*14in)\)

\(\displaystyle SA=(950.4in^{2})+(504in^{2})+(739.2in^{2})\)

\(\displaystyle SA=2193.6in^{2}\)

If you calculated the surface area to equal \(\displaystyle 6652.8in^{2}\), then you utilized the volume formula of a rectangular prism, which is \(\displaystyle V=l*w*h\); this is incorrect.

A few facts need to be known to solve this problem. Observe that the diagonal of the square face of the cube cuts it into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse: \(\displaystyle 1:\sqrt{2}\).

\(\displaystyle \frac{s}{d}=\frac{1}{\sqrt{2}}\)

\(\displaystyle \dpi{100} \dpi{100} \frac{s}{4.2cm}=\frac{1}{\sqrt{2}}\)

Rearrange an solve for \(\displaystyle s\).

\(\displaystyle \dpi{100} s=\frac{4.2cm}{\sqrt{2}}\)

Now, solve for the area of the cube using the formula \(\displaystyle \dpi{100} \dpi{100} SA=6(s^{2})\).

\(\displaystyle SA=6*(\frac{4.2cm}{\sqrt{2}})^{2}\)

\(\displaystyle SA=\frac{6}{1}*(\frac{4.2cm}{\sqrt{2}}*\frac{4.2cm}{\sqrt{2}})\)

\(\displaystyle \dpi{100} SA=\frac{6}{1}*(\frac{17.64cm^{2}}{2})\)

\(\displaystyle \dpi{100} \dpi{100} SA=3*17.64cm^{2}\)

\(\displaystyle \rightarrow 52.92cm^{2}\)

The surface area of a cube is the sum of the area of each face.  Since there are 6 faces on a cube, the surface area of the entire cube is \(\displaystyle 6\cdot16\).

To find the surface area of a cube, square the length of one edge and multiply the result by six: \(\displaystyle 6(a^{2})\)

\(\displaystyle 6(4^{2})=6(16)=96\)

To find the surface of a cube, use the standard equation: 

\(\displaystyle SA=6a^2\)

where \(\displaystyle a\) denotes the side length.

Plug in the given value for \(\displaystyle a\) to find the answer:

\(\displaystyle SA=6\cdot \left(\frac{3}{2}\right)^2=6\cdot \left(\frac{9}{4}\right)=\frac{27}{2}\)

Remember, \(\displaystyle 6\; in=0.50\; ft\).

For a cube:

\(\displaystyle SA = 6s^{2}\)

Thus \(\displaystyle 6(0.50)^{2}=6(0.25)=1.50\; ft^{2}\).