Shop Essentials (Applied Mathematics)

Geometry: Circles and Polygons 171

Geometry: Circles and Polygons covers the specifics of geometry involving circles and polygons with any number of sides. The class includes a discussion on the internal angles of a circle as well as the method to calculate the circumference and area of a circle. Additionally, this class covers the calculation of missing angles in any polygon

Circles and polygons, along with triangles, are the basic building blocks of any geometric figure. Knowledge of the calculations and uses of circles and polygons can prove useful when working with prints in any number of manufacturing capacities.

  • Difficulty Beginner

  • Format Online

  • Number of Lessons 16

  • Language English


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Course Outline
  • Circles
  • Semicircles
  • Radius and Diameter
  • Circumference
  • Area of a Circle
  • Circles Review
  • Angles and Circles
  • Angles and Circles: Sample Problem
  • Tangents
  • Tangents: Sample Problem
  • Angles and Tangents Review
  • Polygons
  • Types of Polygons
  • Interior Angles
  • Polygons: Sample Problem
  • Polygons Review
  • Describe the basic properties of a circle.
  • Describe the basic properties of a semicircle.
  • Contrast radius and diameter.
  • Calculate the circumference of a circle.
  • Calculate the area of a circle.
  • Describe the angles of a circle.
  • Solve for missing angles in a bolt circle problem.
  • Define tangent.
  • Solve for a missing angle in a tangent problem.
  • Define polygon.
  • Describe the types of polygons.
  • Describe the characteristics of polygons’ interior angles.
  • Solve for a missing angle in a polygon problem.
Vocabulary Term


The combination of either two rays with the same endpoint or two straight lines that intersect. Angles are measured in degrees, which specify the amount of separation between the sides of the angle.

angles of a circle

The angles formed within a circle that share the circle's center point as the vertex. All angles in a circle add up to 360 degrees.


The size of the space contained within an enclosed two-dimensional figure. Area is typically measured in square units such as square inches or square centimeters.


The instructions and drawings that are used to manufacture a part. Using blueprints effectively requires a good understanding of mathematics.

bolt circle

A set of holes that appear in a circular formation on a workpiece. Bolt circles are also known as bolt hole patterns.

bolt hole pattern

A set of holes that appear in a circular formation on a workpiece. Bolt hole patterns are also known as bolt circles.

central angle

An angle formed within a circle in which the center of the circle is the vertex. The sides of the angle are radii.


The figure formed by the group of points that are an equal distance from a central point. The angles of a circle add up to 360 degrees.


The boundary or perimeter around a circle. Circumference measures the distance around a circle.

concave polygons

A polygon in which at least one of the angles is greater than 180 degrees. Only polygons with four or more sides can be concave polygons.

convex polygons

A polygon in which all interior angles are less than or or equal to 180 degrees. Most regular polygons are convex polygons.


The distance from one edge of a circle to the opposite edge through the center. The diameter divides the circle in half.


A representation of a known equation using letters, numbers, and/or symbols. Common formulas are used to find the area or volume of shapes such as circles and cubes.


A polygon with six sides.

infinite decimal number

A decimal number that has no end and no repeating pattern. The most commonly known infinite decimal number is pi.


The point at which lines, line segments, or rays cross or overlap. The intersection of any lines, segments, or rays forms a set of angles.


A series of points that extends endlessly in two directions. A line is perfectly straight, and its length cannot be measured.

line segment

A section of a line with two endpoints that indicate where the section ends. The length of a line segment can be measured.


A polygon with more than 12 sides. 'N' can be replaced with the number of sides the polygon has.


Extending in the same direction and equidistant at all points. Parallel lines never intersect.


An intersection of two lines or objects at right angles. A radius of a circle drawn to a point of tangency is always perpendicular to the tangent line.


Intersecting at right angles. Two perpendicular lines form four of these right angles.


A special constant value that relates the diameter of a circle to its circumference. Pi is roughly 3.14 and is used to find the circumference and area of a circle.


A dot that indicates a definite position or location. A point has no width, depth, or length.

point of tangency

The point at which a tangent touches the circle, also known as a tangent point. A radius drawn to the point of tangency is always perpendicular to the tangent line.


A closed shape that has at least three sides. Triangles, quadrilaterals, rectangles, and squares are all types of polygons.


A polygon with four sides. Squares and rectangles are quadrilaterals.


The distance from the center to the edge of a circle. All radii of a circle are equal in length.


A portion of a line that has only one endpoint and extends endlessly in one direction. The length of a ray cannot be measured.

regular polygons

A polygon in which all angles and sides are equal. Equilateral triangles and squares are examples of regular polygons.


A half-circle. The angles of a semicircle add up to 180 degrees.

square inches

A unit of area measurement that is equal to a square with sides that are one inch long. Square inches are found by multiplying the square’s length and height, which is the same as squaring 1 inch (1² ).


A line, line segment, or ray that touches a circle at exactly one point. Tangents often appear in blueprints when a cylindrical object touches a flat surface.

tangent point

The point at which a tangent touches the circle, also known as a point of tangency. A radius drawn to the tangent point is always perpendicular to the tangent line.


The point where the two sides of an angle meet. On some prints, an angle may be identified only by its vertex.

vertical angles

Two angles that share the same vertex and are positioned directly opposite one another. Vertical angles are formed whenever two lines intersect.