By taking the difference between the areas of the large rectangle and the area of the small rectangle, we conclude that the area of the border is 100 square meters.
How to get the area of the border of the pool?
The area of the border will be equal to the difference between the area of the large rectangle and the area of the smaller rectangle.
Remember that for a rectangle of length L and width W, the area is:
A = L*W
Also, remember that the distance between two points (a, b) and (c, d) is:
[tex]D = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
For the large distance, we define the length as the distance between the vertices (9, 0) and (0, 12), so we have:
[tex]L = \sqrt{9^2 + 12^2 } = 15[/tex]
And the width as the distance between (9, 0) and (17, 6), then we have:
[tex]W = \sqrt{(17 - 9)^2 + (0 - 6)^2} = 10[/tex]
Then the area is:
A = 15*10 = 150 square units.
For the smaller rectangle, the length is the distance between (9, 4) and (3, 12)
[tex]L' = \sqrt{(9 - 3)^2 + (4 - 12)^2} = 10[/tex]
And the width is the distance between (9, 4) and (13, 7).
[tex]W' = \sqrt{(9 - 13)^2 + (7 - 4)^2} = 5[/tex]
So the area is:
A' = 10*5 = 50
Then the area of the border is:
A - A' = 150 - 50 = 100 square units.
If you want to learn more about areas:
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