Solution

The region represented by the larger rectangle is the garden and the walkway combined. The length of the region is the length of the garden plus twice the width of the walkway, or feet. The width of the region is the 18+(2)(3)=24 width of the garden plus twice the width of the walkway, or feet. 12+(2)(3)=18
Therefore, the area of the region represented by the larger rectangle is (24)(18), or 432 square feet, and the area of the walkway is or \(216\) square feet.

Let's first add some lines to divide the walkway into 4 rectangular regions (A, B, C and D), and then find the area of each region.


We'll start with region A.
Since the walkway is uniformly 3 feet wide, we can add this to our diagram.
We'll also add the fact that the garden is 18 feet long.



At this point, we can see that the total length of region A = 18 + 3 + 3 = 24 feet

So, the area of region A = (3)(24) = 72
Since region B is identical to region A, we know that the area of region B = 72 also


Now let's examine region C.

We can see that the dimensions of region C are 3 by 12
So, the area of region C = (3)(12) = 36
Since region D is identical to region C, we know that the area of region D = 36 also

TOTAL AREA of walkway = 72 + 72 + 36 + 36 = 216

Answer: 216

Cheers,
Brent
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(18+6)x(12+6)-18x12 = 216 ans.

Hi,

Just one question, why we are adding length and width of garden when we have to find the area of only walkway?
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In order to find the area of a rectangle, we need the length and the width.
In a few places in my solution, we don't necessarily know the length and width.
Define those values, we sometimes have to add a few lengths together.

For example, in my solution, I write: At this point, we can see that the total length of region A = 18 + 3 + 3 = 24 feet

Does that help?
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