Question

find the perimeter and area of this figure. p =? units a = units²

Explanation:

Step1: Identify the side - length using the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let's assume the vertices of the rhombus are $(2,5),(4,8),(6,5),(4,2)$. Taking two adjacent vertices, say $(2,5)$ and $(4,8)$:
$d=\sqrt{(4 - 2)^2+(8 - 5)^2}=\sqrt{2^2+3^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.61$.

Step2: Calculate the perimeter

Since a rhombus has 4 equal - length sides, the perimeter $P = 4d$. Substituting $d=\sqrt{13}$, we get $P = 4\sqrt{13}\approx4\times3.61 = 14.42$ units.

Step3: Calculate the area

The area of a rhombus is given by $A=\frac{1}{2}d_1d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals. The length of one diagonal (vertical) is from $(2,5)$ to $(6,5)$, so $d_1=4$. The length of the other diagonal (horizontal) is from $(4,2)$ to $(4,8)$, so $d_2 = 6$. Then $A=\frac{1}{2}\times4\times6=12$ square units.

Answer:

$P\approx14.42$ units, $A = 12$ units$^2$