Let's go step-by-step to fill out the table with the given conditions:
### Quadrilateral:
- Number of Sides: 4
- Side Length: 5 units
Calculations:
- Perimeter: To find the perimeter, we multiply the number of sides by the side length.
[tex]\[
Perimeter = 4 \times 5 = 20 \text{ units}
\][/tex]
- Area: The area of a regular quadrilateral (square) is calculated by squaring the side length.
[tex]\[
Area = 5^2 = 25.0 \text{ units}^2
\][/tex]
### Pentagon:
- Number of Sides: 5
- Side Length: 4 units
Calculations:
- Perimeter:
[tex]\[
Perimeter = 5 \times 4 = 20 \text{ units}
\][/tex]
- Area:
[tex]\[
Area \approx 27.53 \text{ units}^2
\][/tex]
### Decagon:
- Number of Sides: 10
- Side Length: 2 units
Calculations:
- Perimeter:
[tex]\[
Perimeter = 10 \times 2 = 20 \text{ units}
\][/tex]
- Area:
[tex]\[
Area \approx 30.78 \text{ units}^2
\][/tex]
### Icosagon:
- Number of Sides: 20
- Side Length: 1 unit
Calculations:
- Perimeter:
[tex]\[
Perimeter = 20 \times 1 = 20 \text{ units}
\][/tex]
- Area:
[tex]\[
Area \approx 31.57 \text{ units}^2
\][/tex]
Given these calculations, we can complete the table as follows:
\begin{tabular}{|c|c|c|c|c|}
\hline Regular Figure & \begin{tabular}{l}
Number of \\
Sides
\end{tabular} & \begin{tabular}{l}
Side \\
Length
\end{tabular} & Perimeter & Area \\
\hline quadrilateral & 4 & 5 & 20 units & 25.0 units[tex]$^2$[/tex] \\
\hline pentagon & 5 & 4 & 20 units & 27.53 units[tex]$^2$[/tex] \\
\hline decagon & 10 & 2 & 20 units & 30.78 units[tex]$^2$[/tex] \\
\hline icosagon & 20 & 1 & 20 units & 31.57 units[tex]$^2$[/tex] \\
\hline
\end{tabular}
