What is polygon ?
A polygon can be defined as a flat or plane, two-dimensional closed shape with straight sides. It does not have curved sides.
Regular polygon :
A polygon having equal sides and equal angles is a regular polygon.
To find area of regular polygon, we use the formula
What is Apothem ?
A line from the center of a regular polygon at right angles to any of its sides.
Find the area of each of regular polygon.
Problem 1 :
Solution :
Number of sides of the given polygon = 6
∠AOB = 360/6 ==> 60
∠COB = 60/2 ==> 30
Apothem = OC
tan θ = BC/OC
tan 30 = 9/OC
0.577 = 9/OC
OC = 9/0.577
OC = 15.59 (Apothem)
Perimeter of the polygon = 618) ==> 108 ft
Area of polygon = (1/2) x Perimeter x apothem
Area of polygon = (1/2) x 108 x 15.59
= 841.86 ft^{2}
Problem 2 :
Solution :
Number of sides of the given polygon = 3
∠AOB = 360/3 ==> 120
∠COB = 120/2 ==> 60
In triangle OCB :
Apothem = OC
tan θ = BC/OC
tan 60 = 4/OC
1.732 = 4/OC
OC = 4/1.732
OC = 2.309
OC = 2.309 (Apothem)
Perimeter of the polygon = 3(4) ==> 12 inches
Area of polygon = (1/2) x Perimeter x apothem
Area of polygon = (1/2) x 12 x 2.309
= 13.854 square inches
Problem 3 :
Solution :
Number of sides of the given polygon = 6
∠AOB = 360/6 ==> 60
∠COB = 60/2 ==> 30
In triangle OCB :
Apothem = OC
tan θ = BC/OC
tan 30 = 6/OC
0.577 = 6/OC
OC = 6/0.577
OC = 10.39
OC = 10.39 (Apothem)
Perimeter of the polygon = 6(12) ==> 72 inches
Area of polygon = (1/2) x Perimeter x apothem
Area of polygon = (1/2) x 72 x 10.39
= 374.04 square meter
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM