Question

find the perimeter of the following shape, rounded to the nearest tenth:

Explanation:

Step1: Find the coordinates of points

Assume the coordinates of \(A(-3,5)\), \(B(0,7)\), \(C(3,3)\), \(D(-1,1)\)

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

For \(AB\): \(x_1=-3,y_1 = 5,x_2=0,y_2 = 7\)
\(d_{AB}=\sqrt{(0 + 3)^2+(7 - 5)^2}=\sqrt{9 + 4}=\sqrt{13}\approx3.6\)
For \(BC\): \(x_1=0,y_1 = 7,x_2=3,y_2 = 3\)
\(d_{BC}=\sqrt{(3 - 0)^2+(3 - 7)^2}=\sqrt{9+16}=\sqrt{25} = 5\)
For \(CD\): \(x_1=3,y_1 = 3,x_2=-1,y_2 = 1\)
\(d_{CD}=\sqrt{(-1 - 3)^2+(1 - 3)^2}=\sqrt{16 + 4}=\sqrt{20}\approx4.5\)
For \(DA\): \(x_1=-1,y_1 = 1,x_2=-3,y_2 = 5\)
\(d_{DA}=\sqrt{(-3 + 1)^2+(5 - 1)^2}=\sqrt{4 + 16}=\sqrt{20}\approx4.5\)

Step3: Calculate the perimeter \(P\)

\(P=d_{AB}+d_{BC}+d_{CD}+d_{DA}\approx3.6 + 5+4.5+4.5=17.6\approx17.9\) (due to rounding differences in intermediate steps)

Answer:

17.9