Question

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

Explanation:

Step1: Find the side length using distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Take two adjacent points, say \((1,5)\) and \((2,7)\). Then \(d=\sqrt{(2 - 1)^2+(7 - 5)^2}=\sqrt{1 + 4}=\sqrt{5}\approx2.24\).

Step2: Calculate the perimeter

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

Step3: Calculate the area using diagonals

The diagonals of the rhombus: One diagonal (vertical - like between \((2,7)\) and \((2,3)\)) has length \(l_1=7 - 3 = 4\). The other diagonal (horizontal - like between \((1,5)\) and \((5,5)\)) has length \(l_2=5 - 1 = 4\). The area formula for a rhombus \(A=\frac{1}{2}l_1l_2\). Substituting \(l_1 = 4\) and \(l_2 = 4\), \(A=\frac{1}{2}\times4\times4 = 8\).

Answer:

\(P = 8.96\) units, \(A = 8\) units²