find the perimeter and area of this figure.\np = ? units\na = units²\nround your answer to the nearest…

Explanation:

Step1: Find the length of one side

Use the distance formula (d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}). Take two adjacent points, say ((1,5)) and ((3,7)). (d=\sqrt{(3 - 1)^2+(7 - 5)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83)

Step2: Calculate the perimeter

Since it's a rhombus (all sides equal), (P = 4d). (P=4\times\sqrt{8}\approx4\times2.83 = 11.32)

Step3: Calculate the area

Use the formula for the area of a rhombus (A=\frac{1}{2}d_1d_2). The diagonals (d_1=(7 - 3)\times2 = 8) (vertical distance between ((3,7)) and ((3,3))) and (d_2=(5 - 1)\times2 = 8) (horizontal distance between ((1,5)) and ((5,5))). (A=\frac{1}{2}\times4\times4 = 8)

Answer:

(P = 11.32) units, (A = 8) units²