2 Answers

Sweeeeeet · Answer 1 · 2021-02-01T11:27:48+0000

Answer:

The perimeter of the figure is 46.3 units, approximately.

Explanation:

To find the perimeter of this figure, we need to use the formula

$d=\sqrt{(y_(2) -y_(1) )^(2) +(x_(2)-x_(1) )^(2) }$ , which gives the distance between two points.

P(-3,2) and
O(0,-6) .

Using the formula, we have

$d_(PO)=\sqrt{(-6-2)^(2)+(0-(-3))^(2) } =\sqrt{(-8)^(2)+(3)^(2) }\\ d_(PO)=√(64+9)=√(73) \approx 8.5$

The distance from P to O is around 8.5 units.

P(-3,2) and
Y(6,-2) .

$d_(PY) =\sqrt{(-2-2)^(2)+(6-(-3))^(2) }=\sqrt{(-4)^(2)+(9)^(2)} =√(16+81)\\ d_(PY) =√(97) \approx 9.8$

The distance from P to Y is around 9.8 units.

Y(6,-2) and
R(3,-6)

$d_(YR) =\sqrt{(-6-(-2))^(2)+(3-6)^(2) }=\sqrt{(-4)^(2)+(-3)^(2)} =√(16+9)\\ d_(PY) =√(25) = 5$

The distance from Y to R is 25 units.

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.

$P \approx 8.5+9.8+25+3 \approx 46.3$

Therefore, the perimeter of the figure is 46.3 units, approximately.