how would you find the area of the walk

Question

A 12m by 15m rectangular garden has a walk 1m wide Around it. How would you find the area of the walk? 

Answer 1

I'm going to start out by describing something that might not seem related, but it is.  Let's imagine that you have a rectangle, and you cut a smaller rectangle out of the center.  The area remaining is the area of the rectangle before you've cut the piece out, minus the area of the piece you've removed.  Easy so far, right?

 

Now, we can imagine the area of the garden and the walk together as the bigger rectangle.  We can find the area of the walk by subtracting the area of the garden.  This leaves behind only the area of the walk.

 

The area of the garden is easier to calculate, so let's start there.  Let's call this A1. The formula for the area of rectangle is

A = L*W.  We can use this to solve for A1:

 

A1 = 12 * 15 = 180.

 

Now let's examine the area of the garden and walk together, and call it A2.  The walk extends 1 m beyond the garden, on all sides.  So how wide is that, and how long?  Well, let's say that lengthwise, the garden is L.

If we start walking from the left hand side of A2, we have to pass 1 meter before we arrive at the left-hand side of A1.  We then have to walk L meters before we reach the right-hand side of the garden, at which point the walk begins again.  We have to walk another meter before we reach the right-hand side of A2. 

 

From this, we see that the length of A2 is 1 + L + 1 = L + 2.

Similar logic will show that the width of A2 is 1 + W + 1 = W + 2.

 

Putting this together, the area of A2 is (L+2)(W+2) = (12 + 2)(15 + 2)

=14*17.

 

To find the area of the walk (A), we subtract the area of the garden from the area of the walk and garden together:

A = A2 - A1.

 

Plug in the numbers, and you're done!