Question

The coordinate plane shows the floor plan for a swimming pool. What is the area of the pool’s border?"

Answer 1

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

$Distance = \sqrt{\left ( c - a \right )^{2} + \left ( d - b \right )^{2}}$

So, the length of pool + border

= $Distance = \sqrt{\left ( 9 - 0 \right )^{2} + \left ( 0 - 12 \right )^{2}}$

Length of pool + border = 15 m

the width of pool + border

= $Distance = \sqrt{\left ( 17 - 9 \right )^{2} + \left ( 6 - 0 \right )^{2}}$

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

= $Distance = \sqrt{\left ( 3 - 9 \right )^{2} + \left ( 12 - 4 \right )^{2}}$

Length of pool + border = 10 m

the width of pool

= $Distance = \sqrt{\left ( 13 - 9 \right )^{2} + \left ( 7- 4 \right )^{2}}$

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.

Answer 2

A = Area
L= Length = 15
W + widith = 10
A = 150
The pool area is L = 10
w= 5
A= 50
So the area of the perimeter = 100 square meters