To solve the given problem, we will determine the perimeter and area of each quadrilateral based on the provided coordinates.
### Quadrilateral 1: Vertices [tex]\( A(0,0) \)[/tex], [tex]\( B(6,0) \)[/tex], [tex]\( C(6,4) \)[/tex], [tex]\( D(0,4) \)[/tex]
1. Perimeter:
- [tex]\( AB = \sqrt{(6-0)^2 + (0-0)^2} = 6 \)[/tex] units
- [tex]\( BC = \sqrt{(6-6)^2 + (4-0)^2} = 4 \)[/tex] units
- [tex]\( CD = \sqrt{(0-6)^2 + (4-4)^2} = 6 \)[/tex] units
- [tex]\( DA = \sqrt{(0-0)^2 + (4-0)^2} = 4 \)[/tex] units
Total Perimeter: [tex]\( 6 + 4 + 6 + 4 = 20 \)[/tex] units
2. Area:
- This is a rectangle where the length is 6 units and the width is 4 units.
Area: [tex]\( 6 \times 4 = 24 \)[/tex] square units
### Quadrilateral 2: Vertices [tex]\( A(0,0) \)[/tex], [tex]\( B(5,0) \)[/tex], [tex]\( C(8,4) \)[/tex], [tex]\( D(3,4) \)[/tex]
1. Perimeter:
- [tex]\( AB = \sqrt{(5-0)^2 + (0-0)^2} = 5 \)[/tex] units
- [tex]\( BC = \sqrt{(8-5)^2 + (4-0)^2} = 5 \)[/tex] units
- [tex]\( CD = \sqrt{(3-8)^2 + (4-4)^2} = 5 \)[/tex] units
- [tex]\( DA = \sqrt{(0-3)^2 + (4-0)^2} = 5 \)[/tex] units
Total Perimeter: [tex]\( 5 + 5 + 5 + 5 = 20 \)[/tex] units
2. Area:
- This is a parallelogram with a base of 5 units and height of 4 units.
Area: [tex]\( 5 \times 4 = 20 \)[/tex] square units
### Quadrilateral 3: Vertices [tex]\( A(0,0) \)[/tex], [tex]\( B(5,0) \)[/tex], [tex]\( C(5,5) \)[/tex], [tex]\( D(0,5) \)[/tex]
1. Perimeter:
- [tex]\( AB = \sqrt{(5-0)^2 + (0-0)^2} = 5 \)[/tex] units
- [tex]\( BC = \sqrt{(5-5)^2 + (5-0)^2} = 5 \)[/tex] units
- [tex]\( CD = \sqrt{(0-5)^2 + (5-5)^2} = 5 \)[/tex] units
- [tex]\( DA = \sqrt{(0-0)^2 + (5-0)^2} = 5 \)[/tex] units
Total Perimeter: [tex]\( 5 + 5 + 5 + 5 = 20 \)[/tex] units
2. Area:
- This is a square with a side length of 5 units.
Area: [tex]\( 5 \times 5 = 25 \)[/tex] square units
### Quadrilateral 4: Vertices [tex]\( A(0,0) \)[/tex], [tex]\( B(1,0) \)[/tex], [tex]\( C(1,9) \)[/tex], [tex]\( D(0,9) \)[/tex]
1. Perimeter:
- [tex]\( AB = \sqrt{(1-0)^2 + (0-0)^2} = 1 \)[/tex] units
- [tex]\( BC = \sqrt{(1-1)^2 + (9-0)^2} = 9 \)[/tex] units
- [tex]\( CD = \sqrt{(0-1)^2 + (9-9)^2} = 1 \)[/tex] units
- [tex]\( DA = \sqrt{(0-0)^2 + (9-0)^2} = 9 \)[/tex] units
Total Perimeter: [tex]\( 1 + 9 + 1 + 9 = 20 \)[/tex] units
2. Area:
- This is a rectangle where the length is 1 unit and the width is 9 units.
Area: [tex]\( 1 \times 9 = 9 \)[/tex] square units
### In Summary, the table will look like this:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
A & B & C & D & Perimeter & Area \\
\hline
(0,0) & (6,0) & (6,4) & (0,4) & 20 & 24 \\
\hline
(0,0) & (5,0) & (8,4) & (3,4) & 20 & 20 \\
\hline
(0,0) & (5,0) & (5,5) & (0,5) & 20 & 25 \\
\hline
(0,0) & (1,0) & (1,9) & (0,9) & 20 & 9 \\
\hline
\end{tabular}
\][/tex]
