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

1. 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:

$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

Using distance formula, we get

$$AB=\sqrt{(4-(-1))^2+(1-1)^2}$$

$$AB=\sqrt{(4+1)^2+(0)^2}$$

$$AB=\sqrt{(5)^2}$$

$$AB=5$$

Similarly,

$$BC=\sqrt{(4-4)^2+(-2-1)^2}=3$$

$$CD=\sqrt{(-1-4)^2+(-2-(-2))^2}=5$$

$$AD=\sqrt{(-1-(-1))^2+(-2-1)^2}=3$$

Now, perimeter of ABCD is

$$P=AB+BC+CD+AD$$

$$P=5+3+5+3$$

$$P=16$$

Therefore, the perimeter of ABCD is 16 units.