# A rectangular courtyard has a cement walkway around its perimeter. The dimensions of the courtyard are shown in the diagram.

M70500_000_008A.png

Write an expression, in factored form, that represents the area of the cement walkway.

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## Well, it looks like someone's trying to build a walkway around a courtyard. They want to know how to represent the area of that walkway in factored form.

To figure this out, we need to know the dimensions of the courtyard. Unfortunately, I can't see the diagram you mentioned, so I'm just going to have to wing it.

Let's say the length of the courtyard is L and the width is W. Now, if we want to find the area of the entire courtyard, it would be L times W, right?

But we only want to find the area of the walkway, not the whole shebang. So, we need to subtract the area of the courtyard itself from the total area.

Oh, and don't forget that the walkway has a uniform width all around the courtyard. We'll call that width "w".

So, the area of the walkway can be represented as (L+2w)(W+2w) - LW. That's the factored form you're looking for.

Now, if you want the actual value in square yards, you'll need to know the measurements of the courtyard.

In the meantime, I hope this expression helps you walk (or factor) your way to a solution!

## To find the area of the cement walkway, we need to subtract the area of the courtyard from the area of the larger rectangle formed by the outer edge of the walkway.

Let's say the length of the courtyard is L and the width is W. The length of the larger rectangle is equal to the length of the courtyard plus twice the width of the walkway, and the width of the larger rectangle is equal to the width of the courtyard plus twice the width of the walkway.

So the length of the larger rectangle is L + 2W, and the width of the larger rectangle is W + 2W = 3W.

The area of the larger rectangle is then (L + 2W) * (3W), and the area of the courtyard is L * W. To find the area of the walkway, we subtract the area of the courtyard from the area of the larger rectangle:

Walkway Area = (L + 2W) * (3W) - L * W

We can simplify this expression by factoring out a common factor of W:

Walkway Area = W * [(L + 2W) * 3 - L]

Therefore, the expression in factored form that represents the area of the cement walkway is:

Walkway Area = W * (3L + 6W - L)

We can further simplify this expression if needed.

## To find the area of the cement walkway, we need to subtract the area of the courtyard from the area of the enlarged rectangle that includes the walkway.

Let's say the length and width of the courtyard are given as L and W respectively. If we add 2 units to both the length and width to account for the walkway, the dimensions of the enlarged rectangle become L+2 and W+2.

The area of the enlarged rectangle is then (L+2) * (W+2).

The area of the courtyard is given by L * W.

To find the area of the cement walkway, we subtract the area of the courtyard from the area of the enlarged rectangle:

Area of walkway = (L+2) * (W+2) - L * W

Now, we can simplify the expression in factored form:

Area of walkway = L * W + 2L + 2W + 4 - L * W

The simplified expression in factored form representing the area of the cement walkway is:

Area of walkway = 2L + 2W + 4 square units.