Question

A box is 8 1/2 inches wide, 12 3/4 inches long and 5 1/2 inches tall. What is the total surface area of the box?

Answer 1

Answer:

The total surface area of a box is $450\frac{1}{2} \:in^2$.

Step-by-step explanation:

In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object.

A box is most often characterized by its height h, and its width, W, and its length L.

The total surface area of a box is made up of three pairs of sides for a total of six sides and its given by

                                     $A = 2(h \cdot W) + 2(h \cdot L) + 2(W \cdot L)$

We know that the width of a box is 8 1/2 inches, the height of a box is 5 1/2 inches, and the length of a box is 12 3/4 inches.

The total surface area of a box is

$A= 2\left(5\frac{1}{2}\cdot \:8\frac{1}{2}\right)+2\left(5\frac{1}{2}\cdot \:12\frac{3}{4}\right)+2\left(8\frac{1}{2}\cdot \:12\frac{3}{4}\right)\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions} \\\\A=2\left(\frac{11}{2}\cdot \frac{17}{2}\right)+2\left(\frac{11}{2}\cdot \frac{51}{4}\right)+2\left(\frac{17}{2}\cdot \frac{51}{4}\right)\\\\A=\frac{187}{2}+\frac{561}{4}+\frac{867}{4}\\\\A=\frac{901}{2}=450\frac{1}{2}$