Linda has a rectangular cardboard of length 78 cm and perimeter 268 cm.

Question

Linda has a rectangular cardboard of length 78 cm and perimeter 268 cm. She cuts a part of the cardboard to make a cubical box 15 cm long. What is the area of the cardboard left?

Answer 1

In this type of problem it is important to break it into smaller problems.  Here we can break down our task as follows.

Step 1: Find the original area of all the cardboard

Step 2: Find the surface area of the cube that was made

Step 3: Total area of all cardboard will not change by dividing it into pieces, so we can subtract the area found in step 2 from the original area to get the area that the problem asks for.

The first step is easy.  A=L*W.  We know 2L+2W=268, with all units in cm, because a rectangle has four sides and the perimeter is the sum of the side lengths.  We can reduce this equation to L+W=134.  Then solving for W gives

W=134-L=134-78=56

Then the area of the original box is 56*78=4368 square cm.

The second step is somewhat trickier.  It helps to visualize it.  How many sides are there in a cube?  It's easy if you remember a common pair of dice is a pair of cubes and each die has six possible numbers, meaning that a cube has six sides, each of which is a square.

Here, the side length for the cube is 15 cm.  15*15=225 square cm.  We must therefore take six times that amount, giving an area of 1350 square cm for the cube's surface.

To wrap it up, then, we must take the difference of the two areas: 4368-1350=3018.

Answer 2

Sorry, misread original problem. And my iPad doesn't like the editing features