Surface Area of a Cuboid: Finding Area based off Perimeter and Vice Versa

The first step is to calculate the relevant data for all the components of the box.

The length of the box = 6

Given that the height of a cuboid is equal to half its length we are able to deduce the height of the box as follows : 6/2= 3

Hence the height = 3

In order to determine the width, we insert the known data into the formula for the volume of the box:

height*length*width = volume of the cuboid.

3*6*width = 72

18*width=72

We divide by 18:

Hence the width = 4

We are now able to return to the initial question regarding the surface of the cuboid.

Remember that the formula for the surface area is:

(height*length+height*width+length*width)*2

We insert the known data leaving us with the following result:

(3*6+4*3+4*6)*2=

(12+24+18)*2=

(54)*2=

108