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An apothem is a line segment that is drawn from the center of a regular polygon to the midpoint of one of its sides. The word “apothem” comes from the Greek word “apothematos,” which means “the distance from the center.” The apothem of a regular polygon is an important geometric concept that has many applications in mathematics and engineering.

DEFINITIONS:

• Regular Polygon: A regular polygon is a polygon (a closed, two-dimensional shape with straight sides) in which all of the sides are the same length and all of the angles are the same size. Some examples of regular polygons include triangles, squares, pentagons, and hexagons.
• Center: The center of a regular polygon is the point that is equidistant from all of the vertices (corners) of the polygon. In other words, it is the point that is located at the exact center of the polygon.
• Side: A side of a regular polygon is one of the straight lines that forms the boundary of the polygon. For example, a triangle has three sides, a square has four sides, and a hexagon has six sides.
• Midpoint: The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment.

5 EXAMPLES:

1. Triangle: A triangle is a three-sided regular polygon. The center of a triangle is the point where all three medians (lines that connect the midpoint of a side to the opposite vertex) intersect. The apothem of a triangle is the line segment that is drawn from the center of the triangle to the midpoint of one of its sides.
2. Square: A square is a four-sided regular polygon. The center of a square is the point that is equidistant from all four vertices. The apothem of a square is the line segment that is drawn from the center of the square to the midpoint of one of its sides.
3. Pentagon: A pentagon is a five-sided regular polygon. The center of a pentagon is the point that is equidistant from all five vertices. The apothem of a pentagon is the line segment that is drawn from the center of the pentagon to the midpoint of one of its sides.
4. Hexagon: A hexagon is a six-sided regular polygon. The center of a hexagon is the point that is equidistant from all six vertices. The apothem of a hexagon is the line segment that is drawn from the center of the hexagon to the midpoint of one of its sides.
5. Octagon: An octagon is an eight-sided regular polygon. The center of an octagon is the point that is equidistant from all eight vertices. The apothem of an octagon is the line segment that is drawn from the center of the octagon to the midpoint of one of its sides.

10 QUESTION QUIZ:

1. What is an apothem?
2. What is a regular polygon?
3. What is the center of a regular polygon?
4. What is a side of a regular polygon?
5. What is the midpoint of a line segment?
6. What is the apothem of a triangle?
7. What is the apothem of a square?
8. What is the apothem of a pentagon?
9. What is the apothem