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 \((2,5)\) and \((5,3)\).
\(d=\sqrt{(5 - 2)^2+(3 - 5)^2}=\sqrt{9 + 4}=\sqrt{13}\approx3.61\)

Step2: Calculate the perimeter

Since it's a rhombus (all sides equal), \(P = 4d\).
\(P=4\times\sqrt{13}\approx4\times3.61 = 14.44\)

Step3: Calculate the area

Use the formula for the area of a rhombus \(A=\frac{1}{2}\times d_1\times d_2\).
Find the lengths of the diagonals.
Diagonal 1 (vertical - like from \((5,3)\) to \((6,9)\)): \(d_1=\sqrt{(6 - 5)^2+(9 - 3)^2}=\sqrt{1 + 36}=\sqrt{37}\approx6.08\)
Diagonal 2 (horizontal - like from \((2,5)\) to \((9,7)\)): \(d_2=\sqrt{(9 - 2)^2+(7 - 5)^2}=\sqrt{49+4}=\sqrt{53}\approx7.28\)
\(A=\frac{1}{2}\times\sqrt{37}\times\sqrt{53}=\frac{1}{2}\times\sqrt{1961}\approx\frac{1}{2}\times44.28 = 22.14\)

Answer:

\(P = 14.44\) units, \(A = 22.14\) units²