Question

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

Explanation:

Step1: Find the length of one side using the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let's take two adjacent points, say \((2,5)\) and \((4,8)\).

$$
LATEXBLOCK0
$$

Step2: Calculate the perimeter

Since it's a rhombus (all sides equal), \(P = 4d\).

$$ P=4\times\sqrt{13}\approx4\times3.61 = 14.44 $$

Step3: Calculate the area using the formula for the area of a rhombus \(A=\frac{1}{2}d_1d_2\)

The diagonals: \(d_1\) (vertical distance between \((4,2)\) and \((4,8)\)) is \(8 - 2=6\). \(d_2\) (horizontal distance between \((2,5)\) and \((8,5)\)) is \(8 - 2 = 6\).

$$ A=\frac{1}{2}\times6\times6=18 $$

Answer:

\(P = 14.44\) units, \(A = 18\) units²