Identify the polygon that has vertices $$ A(-10,-1) $$, $$ P(-7,3), E(-3,0) $$, and $$ X(-6,-4) $$, and then find the perimeter and area of the polygon. square; $$ P=20 $$ units; $$ A=25 $$ units $$ ^{2} $$ squmbus; $$ P=25 $$ units; $$ A=20 $$ units $$ ^{2} $$ square; $$ P=4 \sqrt{5} $$ units; $$ A=25 $$ units $$ ^{2} $$ rhombus; $$ P=4 \sqrt{5} $$ units; $$ A=20 $$ units $$ ^{2} $$

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To find the perimeter and area of the polygon with vertices $$ A(-10,-1) $$, $$ P(-7,3) $$, $$ E(-3,0) $$, and $$ X(-6,-4) $$, we need to determine the type of polygon first.

Given the coordinates of the vertices, we can plot them on a coordinate plane to visualize the polygon. By plotting the points, we can see that the polygon is a square.

Now, let's calculate the perimeter and area of the square:

1. Perimeter:
The perimeter of a square is given by the formula $$ P = 4 \times \text{side length} $$.

To find the side length, we can use the distance formula between two points. Let's calculate the distance between points $$ A $$ and $$ P $$:
$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Substitute the coordinates of points $$ A $$ and $$ P $$ into the distance formula:
$$ \text{Distance} = \sqrt{(-7 - (-10))^2 + (3 - (-1))^2} $$
$$ \text{Distance} = \sqrt{3^2 + 4^2} $$
$$ \text{Distance} = \sqrt{9 + 16} $$
$$ \text{Distance} = \sqrt{25} $$
$$ \text{Distance} = 5 $$

Therefore, the side length of the square is 5 units.

Now, we can calculate the perimeter:
$$ P = 4 \times 5 $$
$$ P = 20 \text{ units} $$

2. Area:
The area of a square is given by the formula $$ A = \text{side length}^2 $$.

Substitute the side length into the area formula:
$$ A = 5^2 $$
$$ A = 25 \text{ units}^2 $$

Therefore, the perimeter of the square is 20 units, and the area is 25 units^2.
The polygon is a square with a perimeter of 20 units and an area of 25 square units.

Identify the polygon that has vertices ,
, and , and then find
the perimeter and area of the polygon.
square; units; units
squmbus; units; units
square; units; units
rhombus; units; units

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Identify the polygon that has vertices , , and , and then find the perimeter and area of the polygon. square; units; units squmbus; units; units square; units; units rhombus; units; units