Answer:
The perimeter of the figure is 46.3 units, approximately.
Step-by-step explanation:
To find the perimeter of this figure, we need to use the formula
[tex]d=\sqrt{(y_{2} -y_{1} )^{2} +(x_{2}-x_{1} )^{2} }[/tex], which gives the distance between two points.
Distance of PO.
[tex]P(-3,2)[/tex] and [tex]O(0,-6)[/tex].
Using the formula, we have
[tex]d_{PO}=\sqrt{(-6-2)^{2}+(0-(-3))^{2} } =\sqrt{(-8)^{2}+(3)^{2} }\\ d_{PO}=\sqrt{64+9}=\sqrt{73} \approx 8.5[/tex]
The distance from P to O is around 8.5 units.
Distance of PY.
[tex]P(-3,2)[/tex] and [tex]Y(6,-2)[/tex].
[tex]d_{PY} =\sqrt{(-2-2)^{2}+(6-(-3))^{2} }=\sqrt{(-4)^{2}+(9)^{2}} =\sqrt{16+81}\\ d_{PY} =\sqrt{97} \approx 9.8[/tex]
The distance from P to Y is around 9.8 units.
Distance of YR.
[tex]Y(6,-2)[/tex] and [tex]R(3,-6)[/tex]
[tex]d_{YR} =\sqrt{(-6-(-2))^{2}+(3-6)^{2} }=\sqrt{(-4)^{2}+(-3)^{2}} =\sqrt{16+9}\\ d_{PY} =\sqrt{25} = 5[/tex]
The distance from Y to R is 25 units.
Distance of OR.
This is an horizontal side, we don't need to use the formula. The distance from O to R is 3 units.
Now, the perimeter is the sum of all sides.
[tex]P \approx 8.5+9.8+25+3 \approx 46.3[/tex]
Therefore, the perimeter of the figure is 46.3 units, approximately.
