Question

Find the perimeter of the shape below:

Answer 1

Option C : The perimeter is 13.3 units

Explanation:

The coordinates of the given shape is $J(-3,4), K(-1,6), L(1,1)$ and $\mathrm{M}(-1,3)$

To determine the perimeter, first let us find the lengths of the sides using the distance formula,

$d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

The length of JK is given by

$\begin{aligned}J K &=\sqrt{(-1+3)^{2}+(6-4)^{2}} \\&=\sqrt{2^{2}+2^{2}} \\&=\sqrt{4+4} \\&=\sqrt{8}\end{aligned}$

The length of KL is given by

$\begin{aligned}K L &=\sqrt{(1+1)^{2}+(1-6)^{2}} \\&=\sqrt{2^{2}+(-5)^{2}} \\&=\sqrt{4+25} \\&=\sqrt{29}\end{aligned}$

The length of LM is given by

$\begin{aligned}L M &=\sqrt{(-1-1)^{2}+(3-1)^{2}} \\&=\sqrt{(-2)^{2}+(2)^{2}} \\&=\sqrt{4+4} \\&=\sqrt{8}\end{aligned}$

The length of JM is given by

$\begin{aligned}J M &=\sqrt{(-1+3)^{2}+(3-4)^{2}} \\&=\sqrt{(2)^{2}+(-1)^{2}} \\&=\sqrt{4+1} \\&=\sqrt{5}\end{aligned}$

The perimeter of the given shape is

$Perimeter = \ JK \ + \ KL \ + \ LM \ + \ JM$

$Perimeter = \ \sqrt{8} \ + \ \sqrt{29} \ + \sqrt{8} \ + \sqrt{5}$

$Perimeter=13.278$

$Perimeter=13.3 \ units$

Hence, the perimeter is 13.3 units

Thus, Option C is the correct answer.