Question

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

Explanation:

Step1: Calculate the side length

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Take two adjacent points, say \((1,5)\) and \((3,7)\).

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Since it's a rhombus (all sides equal), perimeter \(P = 4\times\) side length.

$$P=4\times2\sqrt{2}=8\sqrt{2}\approx11.31$$

Step2: 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:

\(P = 8\sqrt{2}\approx11.31\) units, \(A = 8\) units²