Question

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

Answer 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.