Identify the polygon with vertices a(5,0), b(2,4), c(−2,1), and d(1,−3), and then find the perimeter and area of the polygon. asap!

Part 1) The polygon is a square

Part 2) The perimeter is equal to

Part 3) The area is equal to

Step-by-step explanation:

we have

Plot the points

see the attached figure

we know that

the formula to calculate the distance between two points is equal to

Find the distance AB

substitute in the formula

Find the distance BC

substitute in the formula

Find the distance CD

substitute in the formula

Find the distance AD

substitute in the formula

we have that

AB=BC=CD=AD

Find the distance BD (diagonal)

substitute in the formula

Verify if the polygon is a square

If the triangle BDA is a right triangle, then the polygon is a square

Applying the Pythagoras theorem

substitute

-----> is true

so

The triangle BDA is a right triangle

therefore

The polygon is a square

Find the Area of the polygon

The area of a square is equal to

we have

Find the perimeter of the polygon

The perimeter of a square is equal to

we have

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