Question

a kite has vertices at (2, 4), (5, 4), (5, 1), and (0, -1). what is the approximate perimeter of the kite? round to the nearest tenth. 11.3 units 13.6 units 16.8 units 20.0 units

Explanation:

Step1: Label vertices & pair equal sides

Let vertices be $A(2,4)$, $B(5,4)$, $C(5,1)$, $D(0,-1)$. Kite has 2 pairs of equal adjacent sides: $AB=CD$, $BC=DA$.

Step2: Calculate length of $AB$

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

$$\begin{align*} AB&=\sqrt{(5-2)^2+(4-4)^2}\\ &=\sqrt{3^2+0^2}=3 \end{align*}$$

Step3: Calculate length of $BC$

$$\begin{align*} BC&=\sqrt{(5-5)^2+(1-4)^2}\\ &=\sqrt{0^2+(-3)^2}=3 \end{align*}$$

Step4: Calculate length of $DA$

$$\begin{align*} DA&=\sqrt{(2-0)^2+(4-(-1))^2}\\ &=\sqrt{2^2+5^2}=\sqrt{4+25}=\sqrt{29}\approx5.385 \end{align*}$$

Step5: Calculate perimeter

Perimeter $=2(AB + DA)=2(3 + 5.385)$

Answer:

16.8 units