Respuesta :

calculista

we know that

The area of a rectangle is equal to

[tex]A=L*W[/tex]

where

L is the length side of the rectangle

W is the width side of the rectangle

see the attached figure with letters to better understand the problem  

The area of the pool's border is equal to the area of rectangle ABCD minus the area of rectangle EFGH

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Step 1

Find the distance AB

Let

[tex]A(0,12)\ B(8,18)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(18-12)^{2}+(8-0)^{2}}[/tex]

[tex]d=\sqrt{(6)^{2}+(8)^{2}}[/tex]

[tex]d=\sqrt{100}[/tex]

[tex]dAB=10\ m[/tex]

Step 2

Find the distance BC

Let

[tex]B(8,18)\ C(17,6)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(6-18)^{2}+(17-8)^{2}}[/tex]

[tex]d=\sqrt{(-12)^{2}+(9)^{2}}[/tex]

[tex]d=\sqrt{225}[/tex]

[tex]dBC=15\ m[/tex]

Step 3

Find the distance EF

Let

[tex]E(3,12)\ F(7,15)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(15-12)^{2}+(7-3)^{2}}[/tex]

[tex]d=\sqrt{(3)^{2}+(4)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]d.EF=5\ m[/tex]

Step 4

Find the distance FG

Let

[tex]F(7,15)\ G(13,7)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(7-15)^{2}+(13-7)^{2}}[/tex]

[tex]d=\sqrt{(-8)^{2}+(6)^{2}}[/tex]

[tex]d=\sqrt{100}[/tex]

[tex]dFG=10\ m[/tex]

Step 5

Find the area of the pool's border

The area of the pool's border is equal to the area of rectangle ABCD minus the area of rectangle EFGH

Area of the rectangle ABCD

[tex]A1=AB*BC=10\ m*15\ m=150\ m^{2}[/tex]

Area of the rectangle EFGH

[tex]A2=EF*FG=5\ m*10\ m=50\ m^{2}[/tex]

Area of the pool's border

[tex]A=A1-A2=150\ m^{2}-50\ m^{2}=100\ m^{2}[/tex]

therefore

the answer is

[tex]100\ m^{2}[/tex]

Ver imagen calculista

The area of the pool’s border is 100 square meters.

Given

The coordinate plane shows the floor plan for a swimming pool.

How to determine the perimeter of a swimming pool?

The perimeter of the swimming pool is given by subtracting the area of the pool from the area of the pool deck to get the exact pool deck area without the pool in it.

The area of the pool is given by;

[tex]\rm Area = length \times width[/tex]

Where the length of the pool is 10 and the width was 5.

Then,

[tex]\rm Area = length \times width\\\\\rm Area = 10 \times 5\\\\\rm Area = 50[/tex]

The area of the pool deck is given by;

The length was 15 and the width was 10.

[tex]\rm Area = length \times width\\\\\rm Area = 15 \times 10\\\\\rm Area = 150[/tex]

Therefore,

The area of the pool’s border is;

= 150 - 50 = 100 square meters

Hence, The area of the pool’s border is 100 square meters.

To know more about Area click the link given below.

https://brainly.com/question/9156074

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