Answer: 85
Step-by-step explanation:
Writing an Equation
Find the length of each side and add them up to get the total perimeter.
We know that there are 6 sides, AB, BC, CD, DE, EF, and FA
We also know that AB = ED and BC = CD = EF = FA
So the total perimeter would be AB + BC + CD + DE + EF + FA = 2AB + 4BC
Finding length of AB
This line goes from (-2,2) to (2,2) so we can find the length by subtracting the x coordinates since the y coordinates are the same
AB = 2 - (-2) = 4
Finding length of BC
Using the Pythagorean Theorem, [tex]a^{2} +b^{2} =BC^{2}[/tex] we can find the length of BC
This line goes from (2,2) to (3,0)
The vertical distance (a) is |0-2| = 2
The horizontal distance (b) is |3-2| = 1
So [tex]2^{2} +1^{2} =BC^{2}[/tex]
[tex]BC^{2} = 5[/tex]
[tex]BC = \sqrt{5}[/tex]
Total length
Using the equation 2AB + 4BC to find the perimeter we get
[tex](2 * 4) + (4 * \sqrt{5} )[/tex]
= [tex]8 +( \sqrt{16} * \sqrt{5} )[/tex]
= [tex]8 + \sqrt{16 * 5}[/tex]
= [tex]8 + \sqrt{80}[/tex]
Since [tex]\sqrt{80}[/tex] is approximately 9, we'll substitute in 9 (assuming we don't have a calculator)
≃ 8 + 9
= 17 units
Converting units
Each unit is 5 yards, so use this ratio get the perimeter in yards
17 units * 5 = 85 yards
