Answer:
Part 1)
or ![P=15.01\ units](https://tex.z-dn.net/?f=P%3D15.01%5C%20units)
Part 2)
or ![P=22.36\ units](https://tex.z-dn.net/?f=P%3D22.36%5C%20units)
Part 3)
or ![P=14.42\ units](https://tex.z-dn.net/?f=P%3D14.42%5C%20units)
Part 4)
or ![P=23.12\ units](https://tex.z-dn.net/?f=P%3D23.12%5C%20units)
Part 5)
or ![P=24.74\ units](https://tex.z-dn.net/?f=P%3D24.74%5C%20units)
Part 6) ![A=36\ units^{2}](https://tex.z-dn.net/?f=A%3D36%5C%20units%5E%7B2%7D)
Part 7) ![A=20\ units^{2}](https://tex.z-dn.net/?f=A%3D20%5C%20units%5E%7B2%7D)
Part 8) ![A=16\ units^{2}](https://tex.z-dn.net/?f=A%3D16%5C%20units%5E%7B2%7D)
Part 9) ![A=10.5\ units^{2}](https://tex.z-dn.net/?f=A%3D10.5%5C%20units%5E%7B2%7D)
Part 10) ![A=6.05\ units^{2}](https://tex.z-dn.net/?f=A%3D6.05%5C%20units%5E%7B2%7D)
Step-by-step explanation:
we know that
The formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
Part 1) we have the triangle ABC
![A(0,3),B(5,1),C(2,-2)](https://tex.z-dn.net/?f=A%280%2C3%29%2CB%285%2C1%29%2CC%282%2C-2%29)
step 1
Find the distance AB
![A(0,3),B(5,1)](https://tex.z-dn.net/?f=A%280%2C3%29%2CB%285%2C1%29)
substitute in the formula
![AB=\sqrt{(1-3)^{2}+(5-0)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%281-3%29%5E%7B2%7D%2B%285-0%29%5E%7B2%7D%7D)
![AB=\sqrt{(-2)^{2}+(5)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%28-2%29%5E%7B2%7D%2B%285%29%5E%7B2%7D%7D)
![AB=\sqrt{29}\ units](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B29%7D%5C%20units)
step 2
Find the distance BC
![B(5,1),C(2,-2)](https://tex.z-dn.net/?f=B%285%2C1%29%2CC%282%2C-2%29)
substitute in the formula
![BC=\sqrt{(-2-1)^{2}+(2-5)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%28-2-1%29%5E%7B2%7D%2B%282-5%29%5E%7B2%7D%7D)
![BC=\sqrt{(-3)^{2}+(-3)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%28-3%29%5E%7B2%7D%2B%28-3%29%5E%7B2%7D%7D)
![BC=\sqrt{18}\ units](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B18%7D%5C%20units)
step 3
Find the distance AC
![A(0,3),C(2,-2)](https://tex.z-dn.net/?f=A%280%2C3%29%2CC%282%2C-2%29)
substitute in the formula
![AC=\sqrt{(-2-3)^{2}+(2-0)^{2}}](https://tex.z-dn.net/?f=AC%3D%5Csqrt%7B%28-2-3%29%5E%7B2%7D%2B%282-0%29%5E%7B2%7D%7D)
![AC=\sqrt{(-5)^{2}+(2)^{2}}](https://tex.z-dn.net/?f=AC%3D%5Csqrt%7B%28-5%29%5E%7B2%7D%2B%282%29%5E%7B2%7D%7D)
![AC=\sqrt{29}\ units](https://tex.z-dn.net/?f=AC%3D%5Csqrt%7B29%7D%5C%20units)
step 4
Find the perimeter
The perimeter is equal to
![P=AB+BC+AC](https://tex.z-dn.net/?f=P%3DAB%2BBC%2BAC)
substitute
![P=[\sqrt{29}+\sqrt{18}+\sqrt{29}]\ units](https://tex.z-dn.net/?f=P%3D%5B%5Csqrt%7B29%7D%2B%5Csqrt%7B18%7D%2B%5Csqrt%7B29%7D%5D%5C%20units)
![P=[2\sqrt{29}+\sqrt{18}]\ units](https://tex.z-dn.net/?f=P%3D%5B2%5Csqrt%7B29%7D%2B%5Csqrt%7B18%7D%5D%5C%20units)
or
![P=15.01\ units](https://tex.z-dn.net/?f=P%3D15.01%5C%20units)
Part 2) we have the rectangle ABCD
![A(-4,-4),B(-2,0),C(4,-3),D(2,-7)](https://tex.z-dn.net/?f=A%28-4%2C-4%29%2CB%28-2%2C0%29%2CC%284%2C-3%29%2CD%282%2C-7%29)
Remember that in a rectangle opposite sides are congruent
step 1
Find the distance AB
![A(-4,-4),B(-2,0)](https://tex.z-dn.net/?f=A%28-4%2C-4%29%2CB%28-2%2C0%29)
substitute in the formula
![AB=\sqrt{(0+4)^{2}+(-2+4)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%280%2B4%29%5E%7B2%7D%2B%28-2%2B4%29%5E%7B2%7D%7D)
![AB=\sqrt{(4)^{2}+(2)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%284%29%5E%7B2%7D%2B%282%29%5E%7B2%7D%7D)
![AB=\sqrt{20}\ units](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B20%7D%5C%20units)
step 2
Find the distance BC
![B(-2,0),C(4,-3)](https://tex.z-dn.net/?f=B%28-2%2C0%29%2CC%284%2C-3%29)
substitute in the formula
![BC=\sqrt{(-3-0)^{2}+(4+2)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%28-3-0%29%5E%7B2%7D%2B%284%2B2%29%5E%7B2%7D%7D)
![BC=\sqrt{(-3)^{2}+(6)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%28-3%29%5E%7B2%7D%2B%286%29%5E%7B2%7D%7D)
![BC=\sqrt{45}\ units](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B45%7D%5C%20units)
step 3
Find the perimeter
The perimeter is equal to
![P=2[AB+BC]](https://tex.z-dn.net/?f=P%3D2%5BAB%2BBC%5D)
substitute
![P=2[\sqrt{20}+\sqrt{45}]\ units](https://tex.z-dn.net/?f=P%3D2%5B%5Csqrt%7B20%7D%2B%5Csqrt%7B45%7D%5D%5C%20units)
or
![P=22.36\ units](https://tex.z-dn.net/?f=P%3D22.36%5C%20units)
Part 3) we have the rhombus ABCD
![A(-3,3),B(0,5),C(3,3),D(0,1)](https://tex.z-dn.net/?f=A%28-3%2C3%29%2CB%280%2C5%29%2CC%283%2C3%29%2CD%280%2C1%29)
Remember that in a rhombus all sides are congruent
step 1
Find the distance AB
![A(-3,3),B(0,5)](https://tex.z-dn.net/?f=A%28-3%2C3%29%2CB%280%2C5%29)
substitute in the formula
![AB=\sqrt{(5-3)^{2}+(0+3)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%285-3%29%5E%7B2%7D%2B%280%2B3%29%5E%7B2%7D%7D)
![AB=\sqrt{(2)^{2}+(3)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%282%29%5E%7B2%7D%2B%283%29%5E%7B2%7D%7D)
![AB=\sqrt{13}\ units](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B13%7D%5C%20units)
step 2
Find the perimeter
The perimeter is equal to
![P=4[AB]](https://tex.z-dn.net/?f=P%3D4%5BAB%5D)
substitute
![P=4[\sqrt{13}]\ units](https://tex.z-dn.net/?f=P%3D4%5B%5Csqrt%7B13%7D%5D%5C%20units)
or
![P=14.42\ units](https://tex.z-dn.net/?f=P%3D14.42%5C%20units)
Part 4) we have the quadrilateral ABCD
![A(-2,-3),B(1,1),C(7,1),D(6,-3)](https://tex.z-dn.net/?f=A%28-2%2C-3%29%2CB%281%2C1%29%2CC%287%2C1%29%2CD%286%2C-3%29)
step 1
Find the distance AB
![A(-2,-3),B(1,1)](https://tex.z-dn.net/?f=A%28-2%2C-3%29%2CB%281%2C1%29)
substitute in the formula
![AB=\sqrt{(1+3)^{2}+(1+2)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%281%2B3%29%5E%7B2%7D%2B%281%2B2%29%5E%7B2%7D%7D)
![AB=\sqrt{(4)^{2}+(3)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%284%29%5E%7B2%7D%2B%283%29%5E%7B2%7D%7D)
![AB=5\ units](https://tex.z-dn.net/?f=AB%3D5%5C%20units)
step 2
Find the distance BC
![B(1,1),C(7,1)](https://tex.z-dn.net/?f=B%281%2C1%29%2CC%287%2C1%29)
substitute in the formula
![BC=\sqrt{(1-1)^{2}+(7-1)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%281-1%29%5E%7B2%7D%2B%287-1%29%5E%7B2%7D%7D)
![BC=\sqrt{(0)^{2}+(6)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%280%29%5E%7B2%7D%2B%286%29%5E%7B2%7D%7D)
![BC=6\ units](https://tex.z-dn.net/?f=BC%3D6%5C%20units)
step 3
Find the distance CD
![C(7,1),D(6,-3)](https://tex.z-dn.net/?f=C%287%2C1%29%2CD%286%2C-3%29)
substitute in the formula
![CD=\sqrt{(-3-1)^{2}+(6-7)^{2}}](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B%28-3-1%29%5E%7B2%7D%2B%286-7%29%5E%7B2%7D%7D)
![CD=\sqrt{(-4)^{2}+(-1)^{2}}](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B%28-4%29%5E%7B2%7D%2B%28-1%29%5E%7B2%7D%7D)
![CD=\sqrt{17}\ units](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B17%7D%5C%20units)
step 4
Find the distance AD
![A(-2,-3),D(6,-3)](https://tex.z-dn.net/?f=A%28-2%2C-3%29%2CD%286%2C-3%29)
substitute in the formula
![AD=\sqrt{(-3+3)^{2}+(6+2)^{2}}](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%28-3%2B3%29%5E%7B2%7D%2B%286%2B2%29%5E%7B2%7D%7D)
![AD=\sqrt{(0)^{2}+(8)^{2}}](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%280%29%5E%7B2%7D%2B%288%29%5E%7B2%7D%7D)
![AD=8\ units](https://tex.z-dn.net/?f=AD%3D8%5C%20units)
step 5
Find the perimeter
The perimeter is equal to
![P=AB+BC+CD+AD](https://tex.z-dn.net/?f=P%3DAB%2BBC%2BCD%2BAD)
substitute
![P=[5+6+\sqrt{17}+8]\ units](https://tex.z-dn.net/?f=P%3D%5B5%2B6%2B%5Csqrt%7B17%7D%2B8%5D%5C%20units)
![P=[19+\sqrt{17}]\ units](https://tex.z-dn.net/?f=P%3D%5B19%2B%5Csqrt%7B17%7D%5D%5C%20units)
or
![P=23.12\ units](https://tex.z-dn.net/?f=P%3D23.12%5C%20units)
Part 5) we have the quadrilateral ABCD
![A(-1,5),B(3,6),C(5,-2),D(1,-3)](https://tex.z-dn.net/?f=A%28-1%2C5%29%2CB%283%2C6%29%2CC%285%2C-2%29%2CD%281%2C-3%29)
step 1
Find the distance AB
![A(-1,5),B(3,6)](https://tex.z-dn.net/?f=A%28-1%2C5%29%2CB%283%2C6%29)
substitute in the formula
![AB=\sqrt{(6-5)^{2}+(3+1)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%286-5%29%5E%7B2%7D%2B%283%2B1%29%5E%7B2%7D%7D)
![AB=\sqrt{(1)^{2}+(4)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%281%29%5E%7B2%7D%2B%284%29%5E%7B2%7D%7D)
![AB=\sqrt{17}\ units](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B17%7D%5C%20units)
step 2
Find the distance BC
![B(3,6),C(5,-2)](https://tex.z-dn.net/?f=B%283%2C6%29%2CC%285%2C-2%29)
substitute in the formula
![BC=\sqrt{(-2-6)^{2}+(5-3)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%28-2-6%29%5E%7B2%7D%2B%285-3%29%5E%7B2%7D%7D)
![BC=\sqrt{(-8)^{2}+(2)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%28-8%29%5E%7B2%7D%2B%282%29%5E%7B2%7D%7D)
![BC=\sqrt{68}\ units](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B68%7D%5C%20units)
step 3
Find the distance CD
![C(5,-2),D(1,-3)](https://tex.z-dn.net/?f=C%285%2C-2%29%2CD%281%2C-3%29)
substitute in the formula
![CD=\sqrt{(-3+2)^{2}+(1-5)^{2}}](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B%28-3%2B2%29%5E%7B2%7D%2B%281-5%29%5E%7B2%7D%7D)
![CD=\sqrt{(-1)^{2}+(-4)^{2}}](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B%28-1%29%5E%7B2%7D%2B%28-4%29%5E%7B2%7D%7D)
![CD=\sqrt{17}\ units](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B17%7D%5C%20units)
step 4
Find the distance AD
![A(-1,5),D(1,-3)](https://tex.z-dn.net/?f=A%28-1%2C5%29%2CD%281%2C-3%29)
substitute in the formula
![AD=\sqrt{(-3-5)^{2}+(1+1)^{2}}](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%28-3-5%29%5E%7B2%7D%2B%281%2B1%29%5E%7B2%7D%7D)
![AD=\sqrt{(-8)^{2}+(2)^{2}}](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%28-8%29%5E%7B2%7D%2B%282%29%5E%7B2%7D%7D)
![AD=\sqrt{68}\ units](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B68%7D%5C%20units)
step 5
Find the perimeter
The perimeter is equal to
![P=\sqrt{17}+\sqrt{68}+\sqrt{17}+\sqrt{68}](https://tex.z-dn.net/?f=P%3D%5Csqrt%7B17%7D%2B%5Csqrt%7B68%7D%2B%5Csqrt%7B17%7D%2B%5Csqrt%7B68%7D)
substitute
![P=2[\sqrt{17}+\sqrt{68}]\ units](https://tex.z-dn.net/?f=P%3D2%5B%5Csqrt%7B17%7D%2B%5Csqrt%7B68%7D%5D%5C%20units)
or
![P=24.74\ units](https://tex.z-dn.net/?f=P%3D24.74%5C%20units)
<h3>The complete answer in the attached file</h3>