Question

use the diagram to find the perimeter and the area of △cde. round your answers to the nearest hundredth.
the perimeter is about
the area is square units.

Explanation:

Step1: Find the lengths of the sides using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

For side $CD$ with $C(4,-1)$ and $D(4,-5)$:
$d_{CD}=\sqrt{(4 - 4)^2+(-5+1)^2}=\sqrt{0 + 16}=4$
For side $DE$ with $D(4,-5)$ and $E(2,-3)$:
$d_{DE}=\sqrt{(2 - 4)^2+(-3 + 5)^2}=\sqrt{(-2)^2+2^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83$
For side $CE$ with $C(4,-1)$ and $E(2,-3)$:
$d_{CE}=\sqrt{(2 - 4)^2+(-3 + 1)^2}=\sqrt{(-2)^2+(-2)^2}=\sqrt{4+4}=\sqrt{8}\approx2.83$

Step2: Calculate the perimeter $P$

$P=d_{CD}+d_{DE}+d_{CE}=4 + 2.83+2.83 = 9.66$

Step3: Calculate the area $A$ using Heron's formula or the formula for a right - angled triangle. Since $CD$ is vertical ($x$-coordinates are the same) and we can consider the base as $CD = 4$ and the height from $E$ to $CD$ (horizontal distance) is $|4 - 2|=2$.

$A=\frac{1}{2}\times base\times height=\frac{1}{2}\times4\times2 = 4$

Answer:

The perimeter is about $9.66$ units.
The area is $4$ square units.