Question

Please help and show work!!

Answer 1

Perimeter = Sum of 4 sides.

But it is a parallelogram. Opposite sides are equal. AB = CD and AC = BD.
So we only need to find the lengths of two sides.

I will find the lengths of AB and BD. You can find any two adjacent sides that you like

$AB = \sqrt{{(4 - ( - 2))}^{2} + {(2 - 2)}^{2} } \\ \\ AB = \sqrt{{(4 + 2)}^{2} + {(0)}^{2} } \\ \\ AB = \sqrt{ {(6)}^{2} } = 6 \: units$

$BD= \sqrt{ {(0 - 4)}^{2} + {( - 1 - 2)}^{2} } \\ \\ BD= \sqrt{ {( - 4)}^{2} + {( - 3)}^{2} } \\ \\ BD= \sqrt{16 + 9} \\ \\ BD= \sqrt{25} = 5 \: units$

So AB = CD = 6 units

BD = AC = 5 units

Perimeter = AB+BD+CD+AC = 6+5+6+5 = 22 Units

Answer is A.

Answer 2

$\huge\mathcal{\fcolorbox{cyan}{black}{\pink{ĄNsWeR࿐}}}$

Perimeter = Sum of 4 sides.

But it is a parallelogram. Opposite sides are equal. AB = CD and AC = BD.

So we only need to find the lengths of two sides.

I will find the lengths of AB and BD. You can find any two adjacent sides that you like

$AB = \sqrt{{(4 - ( - 2))}^{2} + {(2 - 2)}^{2} } \\ \\ AB = \sqrt{{(4 + 2)}^{2} + {(0)}^{2} } \\ \\ AB = \sqrt{ {(6)}^{2} } = 6 \: units$

$BD= \sqrt{ {(0 - 4)}^{2} + {( - 1 - 2)}^{2} } \\ \\ BD= \sqrt{ {( - 4)}^{2} + {( - 3)}^{2} } \\ \\ BD= \sqrt{16 + 9} \\ \\ BD= \sqrt{25} = 5 \: units$

So AB = CD = 6 units

BD = AC = 5 units

Perimeter = AB+BD+CD+AC = 6+5+6+5 = 22 Units

Answer is A.

HOPE SO IT WILL HELP.....