Question

what is the perimeter of the quadrilateral that is graphed below?

round your answer to the nearest whole number.

Explanation:

Step1: Label the vertices

Let the vertices of the quadrilateral be \(A(-6,3)\), \(B(2,3)\), \(C(4, - 1)\), \(D(-4,-1)\)

Step2: Calculate the length of \(AB\)

Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \(A(-6,3)\) and \(B(2,3)\)
\(AB=\sqrt{(2-(-6))^2+(3 - 3)^2}=\sqrt{(8)^2+0^2}=8\)

Step3: Calculate the length of \(BC\)

For \(B(2,3)\) and \(C(4,-1)\)
\(BC=\sqrt{(4 - 2)^2+(-1 - 3)^2}=\sqrt{2^2+(-4)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47\)

Step4: Calculate the length of \(CD\)

For \(C(4,-1)\) and \(D(-4,-1)\)
\(CD=\sqrt{(-4 - 4)^2+(-1+1)^2}=\sqrt{(-8)^2+0^2}=8\)

Step5: Calculate the length of \(DA\)

For \(D(-4,-1)\) and \(A(-6,3)\)
\(DA=\sqrt{(-6+4)^2+(3 + 1)^2}=\sqrt{(-2)^2+4^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47\)

Step6: Calculate the perimeter

Perimeter \(P=AB + BC+CD + DA\)
\(P=8 + 4.47+8+4.47=24.94\approx25\)

Answer:

\(25\)