Question

what is the perimeter of quadrilateral abcd? write your answer as an integer or as a decimal rounded to the nearest tenth. perimeter = units

Explanation:

Step1: Find coordinates of points

Assume \(A(8,5)\), \(B(- 6,-3)\), \(C(-9,-7)\), \(D(0,-7)\)

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

\(AB=\sqrt{(8 + 6)^2+(5 + 3)^2}=\sqrt{14^2+8^2}=\sqrt{196 + 64}=\sqrt{260}\approx16.1\)

Step3: Use distance formula for \(BC\)

\(BC=\sqrt{(-6 + 9)^2+(-3 + 7)^2}=\sqrt{3^2+4^2}=\sqrt{9 + 16}=\sqrt{25}=5\)

Step4: Use distance formula for \(CD\)

\(CD=\sqrt{(0 + 9)^2+(-7+7)^2}=\sqrt{9^2+0^2}=9\)

Step5: Use distance formula for \(DA\)

\(DA=\sqrt{(8 - 0)^2+(5 + 7)^2}=\sqrt{8^2+12^2}=\sqrt{64+144}=\sqrt{208}\approx14.4\)

Step6: Calculate perimeter

Perimeter \(=AB + BC+CD + DA\approx16.1+5 + 9+14.4 = 44.5\)

Answer:

\(44.5\)