Question

use the coordinates to compute the perimeter of the trapezoid. round each calculation to the nearest tenth. (1 point) 16.3 units 12.3 units 14.4 units 13.8 units

Explanation:

Step1: Find the coordinates of each point

From the graph, \(A(0,0)\), \(B(5,0)\), \(C(4,3)\), \(D(1,3)\)

Step2: Calculate the length of \(AB\)

Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \(A(0,0)\) and \(B(5,0)\)
\(AB=\sqrt{(5 - 0)^2+(0 - 0)^2}=\sqrt{25}=5\)

Step3: Calculate the length of \(BC\)

For \(B(5,0)\) and \(C(4,3)\)
\(BC=\sqrt{(4 - 5)^2+(3 - 0)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.2\)

Step4: Calculate the length of \(CD\)

For \(C(4,3)\) and \(D(1,3)\)
\(CD=\sqrt{(1 - 4)^2+(3 - 3)^2}=\sqrt{9}=3\)

Step5: Calculate the length of \(DA\)

For \(D(1,3)\) and \(A(0,0)\)
\(DA=\sqrt{(0 - 1)^2+(0 - 3)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.2\)

Step6: Calculate the perimeter

Perimeter \(P = AB+BC+CD+DA\)
\(P=5 + 3.2+3+3.2=14.4\)

Answer:

14.4 units