Regular Polygons Worksheet

In this regular polygons worksheet, students will explore the properties and characteristics of various geometric shapes. From triangles to hexagons, this worksheet offers a comprehensive review of regular polygons and provides ample practice to help students develop a solid understanding of these shapes. Whether you are a math teacher looking for engaging resources or a student seeking extra practice, this regular polygons worksheet is designed to cater to your needs.

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What is a regular polygon?

A regular polygon is a polygon that has all sides of equal length and all angles of equal measure.

How many sides does a regular hexagon have?

A regular hexagon has 6 sides.

What is the measure of each interior angle in a regular pentagon?

In a regular pentagon, each interior angle measures 108 degrees.

Name a regular polygon that has 12 sides.

A regular polygon with 12 sides is called a dodecagon.

How many diagonals does a regular octagon have?

A regular octagon has 20 diagonals.

What is the sum of the exterior angles in any regular polygon?

The sum of the exterior angles in any regular polygon is always 360 degrees.

Define the term "apothem" in relation to regular polygons.

In relation to regular polygons, an apothem is a line segment that joins the center of the polygon to the midpoint of one of its sides, forming a right angle with that side. The apothem is used to calculate the area of the polygon by multiplying it by the perimeter and dividing by two.

Name a regular polygon that has 20 sides.

A regular polygon with 20 sides is called an icosagon.

How would you calculate the measure of each interior angle in a regular heptagon?

To calculate the measure of each interior angle in a regular heptagon, you can use the formula: (n-2) * 180 / n, where n represents the number of sides. In this case, a heptagon has 7 sides, so you would plug in 7 for n: (7-2) * 180 / 7 = 900 / 7 = 128.57 degrees. Therefore, each interior angle of a regular heptagon measures approximately 128.57 degrees.

Explain how to determine the perimeter of a regular polygon.

To determine the perimeter of a regular polygon, you can use the formula: perimeter = number of sides × length of each side. To find the length of each side, you can use the formula: length of each side = 2 × radius × tan(180°/number of sides). Alternatively, if you know the apothem (distance from the center to the midpoint of a side) and the number of sides, you can use the formula: perimeter = number of sides × length of each side = number of sides × 2 × apothem × tan(180°/number of sides).