This pdf contains:- Regular Pentagon Regular Hexagon Regular Octagon In Euclidean geometry, a regular polygon is a polygon that is equiangular and equilateral. Regular polygons may be either convex or star.
1. Lesson Notes The Perimeter of a Regular Polygon This section will focus on how to calculate Regular Pentagon the Perimeter of a Regular Polygon. We recall that a polygon is regular if all of its sides are congruent and if all its interior angles are congruent. Remember that congruent means identical. The regular polygons that we will focus on in this section are: # of sides(n) = 5 Equilateral Triangle Regular Hexagon # of sides(n) = 3 Square # of sides(n) = 6 Regular Octagon # of sides(n) = 4 # of sides(n) = 8 This resource can be used for FREE by any teacher / 1 student with an active Math Help Services account
2. Lesson Notes Regular Decagon P = ( n )( b ) Finally, we calculate the perimeter (P). P = ( n )( b ) P = (10 )( 3cm ) P = 30cm So, the perimeter of the regular decagon is # of sides(n) = 10 30cm. Let’s try a different type of question where In order to calculate the perimeter of any we are given the perimeter of a regular of the regular polygons, we will use the polygon and we want to calculate the length formula: of one of its sides. P = ( n )( b ) The perimeter of the regular pentagon given below is 35cm. Determine the value of x. “P” is the Perimeter “n” is the number of sides “b” is the side length Let’s try an example using this formula. Calculate the perimeter of the regular decagon given below. First, we state the information that we know about the regular pentagon. P = 35cm n = 5 b=x Next, we state the formula to calculate the perimeter (P) of a regular pentagon. P = ( n )( b ) First, we state the information that we know about the regular decagon. b = 3cm n = 10 Next, we state the formula to calculate the perimeter (P) of a regular decagon. This resource can be used for FREE by any teacher / 2 student with an active Math Help Services account
3. Lesson Notes Finally, we calculate the value of x. Example P = ( n )( b ) 1. Calculate the perimeter of the 35cm = ( 5 )( x ) equilateral triangle below. 35cm ( 5 )( x ) = 5 5 7cm = ( 5 )( x ) 5 x = 7cm Step 1: Statebthe = 7cm information you know So, all of the sides of the regular pentagon about the triangle. measure 7cm in length. n=3 b = 7cm We are ready to do more challenging P = ( n )( b ) examples. n=3 P the Step 2: State ( )( ) n b to calculate = formula b = 7cm the perimeter (P) of an equilateral triangle. n=3 P = ( n )( b ) Step 3: Calculate the perimeter (P). P = ( n )( b ) P = ( 3)( 7cm ) P = 21cm So, the perimeter of the equilateral triangle is 21cm. This resource can be used for FREE by any teacher / 3 student with an active Math Help Services account
4. Lesson Notes 2. The perimeter of the square given below 3. Calculate the perimeter of the regular is 24cm. Determine the value of x. pentagon given below. P = 24cm Step 1: Statenthe =5 information you know Step 1: State the information you know about the pentagon. n=4 about the square. b = 3cm b P= =x 24cm Pn==(5n )( b ) P =n (=n4)( b ) b = 3cm n=5 b=x P = 24cm P the Step 2: State ( )( ) n b to calculate = formula Step 2: State the(formula Pn == 4n )( b ) to calculate the perimeterb(P) = 3cm of a regular pentagon. the perimeterb(P) = xof a square. P = ( n )( b ) P = ( n )( b ) Step 3: Calculate the perimeter (P). Step 3: Calculate the value of x. P = ( n )( b ) P = ( n )( b ) P = ( 5 )( 3cm ) 24cm = ( 4 )( x ) P = 15cm 24cm ( 4 )( x ) So, the perimeter of the regular = pentagon is 15cm. 4 4 6cm = ( 4 )( x ) 4 x = 6cm The value of x is 6cm. This resource can be used for FREE by any teacher / 4 student with an active Math Help Services account
5. Lesson Notes 4. The perimeter of the regular hexagon 5. A regular octagon has a side length of given below is 72cm. Determine the 11cm. Calculate the octagon’s perimeter. value of x. Step 1: State the information you know about the octagon. b = 11cm n=8 Step 2: State the formula to calculate the perimeter of a regular octagon. P = ( n )( b ) Step 3: Calculate the perimeter (P). P = 72cm P = ( n )( b ) Step 1: State the information you know n=6 about the hexagon. P = ( 8 )(11cm ) b=x P = 88cm P = 72cm P =n(=n )( 6 b) So, the perimeter of the regular octagon b=x is 88cm. P = 72cm Pn==(6n )( b ) Step 2: State the formula to calculate the perimeterbof=axregular hexagon. P = ( n )( b ) Step 3: Calculate the value of x. P = ( n )( b ) 72cm = ( 6 )( x ) 72cm ( 6 )( x ) = 6 6 12cm = ( 6 )( x ) 6 x = 12cm The value of x is 12cm. This resource can be used for FREE by any teacher / 5 student with an active Math Help Services account
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