Question

find the perimeter of the shape.

Explanation:

Step1: Identify the coordinates of vertices

Assume \(A(-4, 3)\), \(B(0, 2)\), \(C(2, 4)\), \(D(0, - 3)\).

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

\(AB=\sqrt{(-4 - 0)^2+(3 - 2)^2}=\sqrt{(-4)^2+1^2}=\sqrt{16 + 1}=\sqrt{17}\approx4.12\)

Step3: Find \(BC\)

\(BC=\sqrt{(2 - 0)^2+(4 - 2)^2}=\sqrt{2^2+2^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx2.83\)

Step4: Find \(CD\)

\(CD=\sqrt{(0 - 2)^2+(-3 - 4)^2}=\sqrt{(-2)^2+(-7)^2}=\sqrt{4 + 49}=\sqrt{53}\approx7.28\)

Step5: Find \(DA\)

\(DA=\sqrt{(-4 - 0)^2+(3+3)^2}=\sqrt{(-4)^2+6^2}=\sqrt{16 + 36}=\sqrt{52}=2\sqrt{13}\approx7.21\)

Step6: Calculate the perimeter \(P\)

\(P=AB + BC+CD + DA\approx4.12+2.83+7.28+7.21 = 21.44\approx21.4\)

Answer:

21.4