Let's start by listing out the vertices of the rectangle BCEF
B (0, 3), C (4, -1) , E (2, -3) , F (-2, 1)
The formula for perimeter of a rectangle is given by:
[tex]P=2\left(l+w\right)[/tex]
To calculate the distances BC, CE, EF & FB, we will use the formula for distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} |BC|=\sqrt{(4-0)^2+(-1-3)^2}=\sqrt{16+16}=\sqrt{32} \\ |CE|=\sqrt{(2-4)^2+(-3--1)^2}=\sqrt{4+4}=\sqrt{8} \\ \text{the opposite sides of rectangles are the same} \\ |BC|\equiv|FE|,|CE|\equiv|BF| \end{gathered}[/tex][tex]\begin{gathered} P=2(l+w) \\ P=2(\sqrt{32}+\sqrt{8}) \\ P=16.97units \end{gathered}[/tex]
Perimeter of the rectangle BCEF is 16.97 units
