Question

use the rectangle. round to the nearest tenth.
the perimeter of the rectangle is units.
the area of the rectangle is square units.

Explanation:

Step1: Find the coordinates of the points

Assume \(A=(2,4)\), \(B=(3,1)\), \(C=(8,3)\), \(D=(7,6)\)

Step2: Calculate the length of \(AB\) using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For \(A=(2,4)\) and \(B=(3,1)\):
\(AB=\sqrt{(3 - 2)^2+(1 - 4)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.2\)

Step3: Calculate the length of \(BC\)

For \(B=(3,1)\) and \(C=(8,3)\):
\(BC=\sqrt{(8 - 3)^2+(3 - 1)^2}=\sqrt{25+4}=\sqrt{29}\approx5.4\)

Step4: Calculate the perimeter \(P\) of the rectangle (\(P = 2(l + w)\))

\(P=2(AB + BC)=2(\sqrt{10}+\sqrt{29})\approx2(3.2 + 5.4)=17.2\)

Step5: Calculate the area \(A\) of the rectangle (\(A=l\times w\))

\(A=\sqrt{10}\times\sqrt{29}=\sqrt{290}\approx17.0\)

Answer:

The perimeter of the rectangle is \(17.2\) units. The area of the rectangle is \(17.0\) square units.