Answer :
Alright Fritz and Ditan, let’s work through the activity of exploring regular and irregular polygons step-by-step. Here, we need to fill in the table with information about polygons with the side lengths 5, 6, 8, and 10.
### Step 1: Understanding Polygons
Polygons are shapes with a certain number of sides, and they can be classified as regular (all sides and angles are equal) or irregular (sides and/or angles are not all equal).
### Step 2: Calculating Internal Angles
For a polygon with [tex]\( n \)[/tex] sides, the measure of each internal angle in a regular polygon can be calculated using the formula:
[tex]\[ \text{Internal Angle} = \frac{(n - 2) \times 180^\circ}{n} \][/tex]
### Step 3: Naming the Polygons
Polygon names based on the number of sides:
- [tex]\( 5 \)[/tex] sides: Pentagon
- [tex]\( 6 \)[/tex] sides: Hexagon
- [tex]\( 8 \)[/tex] sides: Octagon
- [tex]\( 10 \)[/tex] sides: Decagon
### Step 4: Classification
Determine if the polygon with the given side lengths and corresponding angles would be classified as regular or irregular.
Now, let’s fill in the table step-by-step:
#### Polygon with 5 sides (Pentagon):
- Length of each side: 5
- Measure of each angle:
[tex]\[ \text{Internal Angle} = \frac{(5 - 2) \times 180^\circ}{5} = \frac{3 \times 180^\circ}{5} = 108^\circ \][/tex]
- Name of the polygon: Pentagon
- Classify: Regular (all internal angles are equal in a regular pentagon)
#### Polygon with 6 sides (Hexagon):
- Length of each side: 6
- Measure of each angle:
[tex]\[ \text{Internal Angle} = \frac{(6 - 2) \times 180^\circ}{6} = \frac{4 \times 180^\circ}{6} = 120^\circ \][/tex]
- Name of the polygon: Hexagon
- Classify: Irregular (though regular hexagons exist, we assume irregular in this case)
#### Polygon with 8 sides (Octagon):
- Length of each side: 8
- Measure of each angle:
[tex]\[ \text{Internal Angle} = \frac{(8 - 2) \times 180^\circ}{8} = \frac{6 \times 180^\circ}{8} = 135^\circ \][/tex]
- Name of the polygon: Octagon
- Classify: Irregular (we assume irregular by default here)
#### Polygon with 10 sides (Decagon):
- Length of each side: 10
- Measure of each angle:
[tex]\[ \text{Internal Angle} = \frac{(10 - 2) \times 180^\circ}{10} = \frac{8 \times 180^\circ}{10} = 144^\circ \][/tex]
- Name of the polygon: Decagon
- Classify: Irregular (we assume irregular by default here)
### Completed Table
Here’s the completed table:
\begin{tabular}{|l|l|l|l|l|}
\hline
& \textbf{Length of} & \textbf{Measure} & \textbf{Name of the} & \textbf{Classify an} \\
& \textbf{each side} & \textbf{of each angle} & \textbf{polygon} & \textbf{regular or irregular polygon} \\
\hline
& \textbf{5} & \textbf{108.0} & \textbf{Pentagon} & \textbf{Regular} \\
\hline
& \textbf{6} & \textbf{120.0} & \textbf{Hexagon} & \textbf{Irregular} \\
\hline
& \textbf{8} & \textbf{135.0} & \textbf{Octagon} & \textbf{Irregular} \\
\hline
& \textbf{10} & \textbf{144.0} & \textbf{Decagon} & \textbf{Irregular} \\
\hline
\end{tabular}
### Conclusion
To complete this activity, you would draw the corresponding polygons on bond paper using a ruler for accurate side lengths and a protractor to measure the angles. This exercise helps to visually and practically understand the properties of regular and irregular polygons. Happy drawing!
### Step 1: Understanding Polygons
Polygons are shapes with a certain number of sides, and they can be classified as regular (all sides and angles are equal) or irregular (sides and/or angles are not all equal).
### Step 2: Calculating Internal Angles
For a polygon with [tex]\( n \)[/tex] sides, the measure of each internal angle in a regular polygon can be calculated using the formula:
[tex]\[ \text{Internal Angle} = \frac{(n - 2) \times 180^\circ}{n} \][/tex]
### Step 3: Naming the Polygons
Polygon names based on the number of sides:
- [tex]\( 5 \)[/tex] sides: Pentagon
- [tex]\( 6 \)[/tex] sides: Hexagon
- [tex]\( 8 \)[/tex] sides: Octagon
- [tex]\( 10 \)[/tex] sides: Decagon
### Step 4: Classification
Determine if the polygon with the given side lengths and corresponding angles would be classified as regular or irregular.
Now, let’s fill in the table step-by-step:
#### Polygon with 5 sides (Pentagon):
- Length of each side: 5
- Measure of each angle:
[tex]\[ \text{Internal Angle} = \frac{(5 - 2) \times 180^\circ}{5} = \frac{3 \times 180^\circ}{5} = 108^\circ \][/tex]
- Name of the polygon: Pentagon
- Classify: Regular (all internal angles are equal in a regular pentagon)
#### Polygon with 6 sides (Hexagon):
- Length of each side: 6
- Measure of each angle:
[tex]\[ \text{Internal Angle} = \frac{(6 - 2) \times 180^\circ}{6} = \frac{4 \times 180^\circ}{6} = 120^\circ \][/tex]
- Name of the polygon: Hexagon
- Classify: Irregular (though regular hexagons exist, we assume irregular in this case)
#### Polygon with 8 sides (Octagon):
- Length of each side: 8
- Measure of each angle:
[tex]\[ \text{Internal Angle} = \frac{(8 - 2) \times 180^\circ}{8} = \frac{6 \times 180^\circ}{8} = 135^\circ \][/tex]
- Name of the polygon: Octagon
- Classify: Irregular (we assume irregular by default here)
#### Polygon with 10 sides (Decagon):
- Length of each side: 10
- Measure of each angle:
[tex]\[ \text{Internal Angle} = \frac{(10 - 2) \times 180^\circ}{10} = \frac{8 \times 180^\circ}{10} = 144^\circ \][/tex]
- Name of the polygon: Decagon
- Classify: Irregular (we assume irregular by default here)
### Completed Table
Here’s the completed table:
\begin{tabular}{|l|l|l|l|l|}
\hline
& \textbf{Length of} & \textbf{Measure} & \textbf{Name of the} & \textbf{Classify an} \\
& \textbf{each side} & \textbf{of each angle} & \textbf{polygon} & \textbf{regular or irregular polygon} \\
\hline
& \textbf{5} & \textbf{108.0} & \textbf{Pentagon} & \textbf{Regular} \\
\hline
& \textbf{6} & \textbf{120.0} & \textbf{Hexagon} & \textbf{Irregular} \\
\hline
& \textbf{8} & \textbf{135.0} & \textbf{Octagon} & \textbf{Irregular} \\
\hline
& \textbf{10} & \textbf{144.0} & \textbf{Decagon} & \textbf{Irregular} \\
\hline
\end{tabular}
### Conclusion
To complete this activity, you would draw the corresponding polygons on bond paper using a ruler for accurate side lengths and a protractor to measure the angles. This exercise helps to visually and practically understand the properties of regular and irregular polygons. Happy drawing!
