I'm guessing the shape is a square because a square has all equal sides, yet I am not sure,

**please help??**
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Brooklyn, NY

You can start off this problem by doing a sketch of the parallelogram, just to have a visual representation.

Secondly, since you need to find the perimeter and area of the parallelogram, that requires knowing the lengths of the sides. Use the distance formula for all sides.

√ = square root, x_{1} = 1st x- coordinate, x_{2} = 2nd x-coordinate, y_{1}=1st y- coordinate, and y_{2} = 2nd y-coordinate

all values are under the square root sign

√(x_{2}-x_{1})² + (y_{2}-y_{1})² = distance formula

so I assigned letters to each coordinate: A(0,3), B(3, 0), C(0, -3) and D(-3, 0)

AB: √(3 - 0)^{2} + (0 - 3)^{2} = √(3)^{2} + (-3)^{2} = √(9) + (9) = √18

BC: √(0 - 3)² +(-3 - 0)² = √(-3)² +(-3)² =√(9) + ( 9) = √18

CD: √(-3 - 0)² +(0 - -3)² = √(-3)² +(3)² = √(9) + (9) = √18

AD: √(-3 - 0)² +(0 - 3)² = √(-3)² +(-3)² =√(9) + (9) = √18

Since all sides are congruent,therefore Its a square.

Area = s^{2} = √18² = 18

Perimeter = add all sides: 4(√18)= 4√18, but in simplest radical form its: 4• √9 •√2 = 4 • 3 •√2 = 12√2

Chicago, IL

It's a square. Area is 18 and perimeter 12√2.

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