Question

1. what is the perimeter of this quadrilateral?

(5, 5)
(2, 4)
poly1
(4, 1)
(6, 1)
3.1 units
10.7 units
12.9 units
7.5 units

Explanation:

Step1: Name vertices & list sides

Vertices: $A(2,4)$, $B(5,5)$, $C(6,1)$, $D(4,1)$. Sides: $AB, BC, CD, DA$.

Step2: Calculate length of AB

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

$$\begin{aligned} AB&=\sqrt{(5-2)^2+(5-4)^2}\\ &=\sqrt{9+1}=\sqrt{10}\approx3.16 \end{aligned}$$

Step3: Calculate length of BC

$$\begin{aligned} BC&=\sqrt{(6-5)^2+(1-5)^2}\\ &=\sqrt{1+16}=\sqrt{17}\approx4.12 \end{aligned}$$

Step4: Calculate length of CD

$$\begin{aligned} CD&=\sqrt{(4-6)^2+(1-1)^2}\\ &=\sqrt{4+0}=2 \end{aligned}$$

Step5: Calculate length of DA

$$\begin{aligned} DA&=\sqrt{(2-4)^2+(4-1)^2}\\ &=\sqrt{4+9}=\sqrt{13}\approx3.61 \end{aligned}$$

Step6: Sum lengths for perimeter

$$\begin{aligned} \text{Perimeter}&=3.16+4.12+2+3.61\\ &\approx12.89\approx12.9 \end{aligned}$$

Answer:

12.9 units