Question

question 8 (multiple choice worth 1 points) (04.03 mc) find the perimeter of the following shape, rounded to the nearest tenth:

Explanation:

Step1: Identify coordinates

Assume \(A(5,5)\), \(B(7,3)\), \(C(3,0)\), \(D(1,2)\)

Step2: Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for \(AB\)

\(x_1 = 5,y_1 = 5,x_2=7,y_2 = 3\), \(AB=\sqrt{(7 - 5)^2+(3 - 5)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx2.83\)

Step3: Use distance formula for \(BC\)

\(x_1 = 7,y_1 = 3,x_2=3,y_2 = 0\), \(BC=\sqrt{(3 - 7)^2+(0 - 3)^2}=\sqrt{16 + 9}=\sqrt{25}=5\)

Step4: Use distance formula for \(CD\)

\(x_1 = 3,y_1 = 0,x_2=1,y_2 = 2\), \(CD=\sqrt{(1 - 3)^2+(2 - 0)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\approx2.83\)

Step5: Use distance formula for \(DA\)

\(x_1 = 1,y_1 = 2,x_2=5,y_2 = 5\), \(DA=\sqrt{(5 - 1)^2+(5 - 2)^2}=\sqrt{16 + 9}=\sqrt{25}=5\)

Step6: Calculate perimeter \(P\)

\(P=AB + BC+CD + DA\approx2.83+5 + 2.83+5=15.66\approx15.7\)

Answer:

15.7