What makes a regular pentagon

Suppose the length of the side is 6 inches. Consider the right triangle POA. The perimeter of a regular or irregular pentagon is the distance around its five sides. Thus, it is the sum of its sides. Based on angle measures and Pentagon sides, it is categorized into regular and irregular Pentagon, Convex, and Concave Pentagon. The table shows the difference between the pentagons. Look at the image below to visualize regular and irregular pentagons along with two other types of pentagons - concave and convex pentagons.

Example 1: Sara measures the pentagon that she has drawn on the ground. She gets each side as 6 feet, and the apothem is 4 feet long. How will she find the area of the grass patch that she is going to grow? Example 2: Mia decides to make a pentagon shape embroidery in her frock.

How much thread will she need to construct a 4 inch sided regular pentagon? Example 3: Help John to find the apothem of the pentagon of the side measure 16 yards. Example 4: Peter found the perimeter of his pentagonal ground to be units. How will he find the area of the ground? A two-dimensional shape with 5 sides is known as a pentagon.

Call the center , and the right end of the diameter. The diameter perpendicular to the original diameter may be constructed by finding the perpendicular bisector. Call the upper endpoint of this perpendicular diameter. For the pentagon, find the midpoint of and call it. Draw , and bisect , calling the intersection point with.

Draw parallel to , and the first two points of the pentagon are and , and copying the angle then gives the remaining points , , and Coxeter , Wells Madachy illustrates how to construct a regular pentagon by folding and knotting a strip of paper. Ball, W. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. Coxeter, H. Introduction to Geometry, 2nd ed. New York: Wiley, pp. DeTemple, D. Monthly 98 , , A convex pentagon has no angles pointing inwards.

Think: concave has a "cave" in it. A pentagon has 5 straight sides. The shape must also be closed all the lines connect up :. Properties of a Pentagon Pentagons can be simple or self-intersection. A self-intersecting regular pentagon is called a pentagram. Lesson Summary Now that you've completed this lesson. You should know: That a pentagon is a five-sided polygon with five angles The identifying properties of a pentagon The different types of pentagons.

Instructor: Malcolm M. Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher. Regular Pentagon In geometry, a pentagon is a five-sided polygon or 5-gon. Local and online.