Answer:
100 m^2
Step-by-step explanation:
For pool + border:
The coordinates of length are (0 m, 12 m) and (9 m, 0 m).
The coordinates of width are (9 m, 0 m) and (17 m, 6 m).
The distance between the two points (a, b) and (c, d) is given by
[tex]Distance = \sqrt{\left ( c - a \right )^{2} + \left ( d - b \right )^{2}}[/tex]
So, the length of pool + border
= [tex]Distance = \sqrt{\left ( 9 - 0 \right )^{2} + \left ( 0 - 12 \right )^{2}}[/tex]
Length of pool + border = 15 m
the width of pool + border
= [tex]Distance = \sqrt{\left ( 17 - 9 \right )^{2} + \left ( 6 - 0 \right )^{2}}[/tex]
Width of pool + border = 10 m
Using the formula for area of rectangle = Length x width
Area of pool + border = 15 x 10 = 150 m^2
For pool only:
The coordinates of length of pool are (9 m, 4 m) and (3 m, 12 m).
The coordinates of width of pool are (9 m , 4 m) and (13 m , 7 m).
So, the length of pool
= [tex]Distance = \sqrt{\left ( 3 - 9 \right )^{2} + \left ( 12 - 4 \right )^{2}}[/tex]
Length of pool + border = 10 m
the width of pool
= [tex]Distance = \sqrt{\left ( 13 - 9 \right )^{2} + \left ( 7- 4 \right )^{2}}[/tex]
Width of pool + border = 5 m
Using the formula for area of rectangle = Length x width
Area of pool = 10 x 5 = 50 m^2
Thus, the area of border = area of pool + border - area of pool = 150 - 50 = 100 m^2.
