Question

find the perimeter of the polygon with the given vertices. round your answer to the nearest hundredth. f(-2,4) a(0,4) e(-2,2) 2 b(2,0) d(0,-2) c(2,-2) 12 the perimeter is about units

Explanation:

Step1: Calculate length of FA

Points $F(-2,4)$ and $A(0,4)$ have same $y -$coordinate. Use distance formula for horizontal line $d=\vert x_2 - x_1\vert$.
$d_{FA}=\vert0 - (-2)\vert= 2$

Step2: Calculate length of AB

Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for points $A(0,4)$ and $B(2,0)$.
$d_{AB}=\sqrt{(2 - 0)^2+(0 - 4)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47$

Step3: Calculate length of BC

Points $B(2,0)$ and $C(2,-2)$ have same $x -$coordinate. Use distance formula for vertical line $d=\vert y_2 - y_1\vert$.
$d_{BC}=\vert-2 - 0\vert = 2$

Step4: Calculate length of CD

Points $C(2,-2)$ and $D(0,-2)$ have same $y -$coordinate. Use distance formula for horizontal line $d=\vert x_2 - x_1\vert$.
$d_{CD}=\vert0 - 2\vert=2$

Step5: Calculate length of DE

Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for points $D(0,-2)$ and $E(-2,2)$.
$d_{DE}=\sqrt{(-2 - 0)^2+(2+ 2)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47$

Step6: Calculate length of EF

Points $E(-2,2)$ and $F(-2,4)$ have same $x -$coordinate. Use distance formula for vertical line $d=\vert y_2 - y_1\vert$.
$d_{EF}=\vert4 - 2\vert=2$

Step7: Calculate perimeter

$P=d_{FA}+d_{AB}+d_{BC}+d_{CD}+d_{DE}+d_{EF}$
$P = 2+4.47+2+2+4.47+2$
$P\approx16.94$

Answer:

$16.94$