Question

find the perimeter and area of this figure. round your answer to the nearest hundredth

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 \(d_1 = 4\) (vertical distance from \(y = 3\) to \(y = 7\)) and \(d_2 = 4\) (horizontal distance from \(x = 1\) to \(x = 5\)).
\(A=\frac{1}{2}\times4\times4 = 8\)

Answer:

\(P = 11.32\) units, \(A = 8.00\) units²