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

The total surface area of a box is
`450(1)/(2) \:in^2`.

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