Question

find the perimeter and area of this figure.
p = ? units
a = units²
round your answer to the nearest hundredth.

Explanation:

Step1: Find the side length using the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Take two adjacent vertices, say $(1,5)$ and $(3,7)$.
$d=\sqrt{(3 - 1)^2+(7 - 5)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83$

Step2: Calculate the perimeter

Since it's a rhombus (all sides equal), $P = 4d$.
$P=4\times\sqrt{8}\approx4\times2.83 = 11.31$

Step3: Calculate the area

Using the formula for the area of a rhombus $A=\frac{1}{2}d_1d_2$.
The diagonals: $d_1=(7 - 3)=4$ (vertical distance) and $d_2=(5 - 1)=4$ (horizontal distance)
$A=\frac{1}{2}\times4\times4 = 8$

Answer:

$P = 11.31$ units, $A = 8$ units²