Question

find the perimeter and area of this figure.
p = ? units
a = units²
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 \((3,5)\) and \((4,3)\).
\(d=\sqrt{(4 - 3)^2+(3 - 5)^2}=\sqrt{1 + 4}=\sqrt{5}\approx2.24\)

Step2: Calculate the perimeter

Since it's a rhombus (all sides equal), \(P = 4d\).
\(P=4\times\sqrt{5}\approx4\times2.24 = 8.96\)

Step3: Calculate the area

Use the formula for the area of a rhombus \(A=\frac{1}{2}d_1d_2\). The diagonals: \(d_1\) (vertical) from \(y = 3\) to \(y = 9\) is \(6\), \(d_2\) (horizontal) from \(x = 3\) to \(x = 9\) is \(6\).
\(A=\frac{1}{2}\times6\times6 = 18\)

Answer:

\(P = 8.96\) units, \(A = 18\) units²