Question

find the approximate perimeter of pentagon abcde plotted below. a(-6,5) b(-2,5) e(-6,1) c(6,0) d(2,-4) choose 1 answer:

Explanation:

Step1: Use distance formula for line - segment length

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of $AB$

For points $A(-6,5)$ and $B(-2,5)$, $x_1=-6,y_1 = 5,x_2=-2,y_2 = 5$.
$AB=\sqrt{(-2+6)^2+(5 - 5)^2}=\sqrt{4^2+0^2}=4$.

Step3: Calculate length of $BC$

For points $B(-2,5)$ and $C(6,0)$, $x_1=-2,y_1 = 5,x_2=6,y_2 = 0$.
$BC=\sqrt{(6 + 2)^2+(0 - 5)^2}=\sqrt{64 + 25}=\sqrt{89}\approx9.43$.

Step4: Calculate length of $CD$

For points $C(6,0)$ and $D(2,-4)$, $x_1=6,y_1 = 0,x_2=2,y_2=-4$.
$CD=\sqrt{(2 - 6)^2+(-4-0)^2}=\sqrt{(-4)^2+(-4)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.66$.

Step5: Calculate length of $DE$

For points $D(2,-4)$ and $E(-6,1)$, $x_1=2,y_1=-4,x_2=-6,y_2 = 1$.
$DE=\sqrt{(-6 - 2)^2+(1 + 4)^2}=\sqrt{(-8)^2+5^2}=\sqrt{64+25}=\sqrt{89}\approx9.43$.

Step6: Calculate length of $EA$

For points $E(-6,1)$ and $A(-6,5)$, $x_1=-6,y_1 = 1,x_2=-6,y_2 = 5$.
$EA=\sqrt{(-6+6)^2+(5 - 1)^2}=\sqrt{0^2+4^2}=4$.

Step7: Calculate perimeter

Perimeter $P=AB + BC+CD+DE+EA$.
$P=4 + 9.43+5.66+9.43+4=32.52\approx32.5$.

Answer:

$32.5$