Question

The surface of the prism is 298 square feet Find the value of x

Answer 1

The rectangular prisma has 6 faces. The area of the front and back faces is

$\begin{gathered} A_1=2\times(7\times x) \\ A_1=14x \end{gathered}$

The area of the base faces is

$\begin{gathered} A_2=2\times7\times4 \\ A_2=56 \end{gathered}$

and the area of the lateral faces is

$\begin{gathered} A_3=2\times4\times x \\ A_3=8x \end{gathered}$

Then, the total surface area is the sum of the above results, that is,

$\begin{gathered} S=A_1+A_2+A_3 \\ S=14x+56+8x \end{gathered}$

By combining similar terms, it gives

$S=22x+56$

Now, from the given information, we know that the surface area must be equal to 298 square feet. So, we have

$22x+56=298$

Then, by subtracting 56 to both sides, we have

$\begin{gathered} 22x=298-56 \\ 22x=242 \end{gathered}$

and by dividing both sides by 22, we get

$\begin{gathered} x=\frac{242}{22} \\ x=11 \end{gathered}$

Therefore, the answer is 11 feet