a kite has vertices at (2, 4), (5, 4), (5, 1), and (0, -1). what is the approximate perimeter of the kite…

Explanation:

Step1: Recall distance formula

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 side - 1 length

Let $(x_1,y_1)=(2,4)$ and $(x_2,y_2)=(5,4)$. Then $d_1=\sqrt{(5 - 2)^2+(4 - 4)^2}=\sqrt{3^2+0^2}=3$.

Step3: Calculate side - 2 length

Let $(x_1,y_1)=(5,4)$ and $(x_2,y_2)=(5,1)$. Then $d_2=\sqrt{(5 - 5)^2+(1 - 4)^2}=\sqrt{0^2+( - 3)^2}=3$.

Step4: Calculate side - 3 length

Let $(x_1,y_1)=(5,1)$ and $(x_2,y_2)=(0,-1)$. Then $d_3=\sqrt{(0 - 5)^2+( - 1 - 1)^2}=\sqrt{( - 5)^2+( - 2)^2}=\sqrt{25 + 4}=\sqrt{29}\approx5.4$.

Step5: Calculate side - 4 length

Let $(x_1,y_1)=(0,-1)$ and $(x_2,y_2)=(2,4)$. Then $d_4=\sqrt{(2 - 0)^2+(4+1)^2}=\sqrt{2^2+5^2}=\sqrt{4 + 25}=\sqrt{29}\approx5.4$.

Step6: Calculate perimeter

$P=d_1 + d_2+d_3 + d_4=3+3 + 5.4+5.4 = 16.8$.

Answer:

16.8 units