Find the perimeter of the polygon with the vertices A (−1, 1), B (4, 1), C (4,−2), and D(−1,−2). The perimeter of ABCD is ___ uni

Question

Find the perimeter of the polygon with the vertices A (−1, 1), B (4, 1), C (4,−2), and D(−1,−2).

The perimeter of ABCD is ___ units.

Could someone explain how I can figure this out?

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Jezebel 1 year 2021-08-19T13:27:38+00:00 1 Answers 20 views 0

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    2021-08-19T13:28:54+00:00

    Given:

    The vertices of a polygon are A (−1, 1), B (4, 1), C (4,−2), and D(−1,−2).

    To find:

    The perimeter of ABCD.

    Solution:

    Distance formula:

    [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

    Using distance formula, we get

    [tex]AB=\sqrt{(4-(-1))^2+(1-1)^2}[/tex]

    [tex]AB=\sqrt{(4+1)^2+(0)^2}[/tex]

    [tex]AB=\sqrt{(5)^2}[/tex]

    [tex]AB=5[/tex]

    Similarly,

    [tex]BC=\sqrt{(4-4)^2+(-2-1)^2}=3[/tex]

    [tex]CD=\sqrt{(-1-4)^2+(-2-(-2))^2}=5[/tex]

    [tex]AD=\sqrt{(-1-(-1))^2+(-2-1)^2}=3[/tex]

    Now, perimeter of ABCD is

    [tex]P=AB+BC+CD+AD[/tex]

    [tex]P=5+3+5+3[/tex]

    [tex]P=16[/tex]

    Therefore, the perimeter of ABCD is 16 units.

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