A hexagon is a closed polygon that consists of six line segments and six internal angles. A regular hexagon is one in which the lengths of all the sides and the measurements of all the angles are equal.
Hexagon Definition
A hexagon is termed as a polygon with six sides. Hexagons are classified into three types: regular hexagons, irregular hexagons, and concave hexagons. A hexagon is called a regular hexagon if all of its sides are equal and all of its angles are the same.
Hexagon Formula
A specified set of formulae for calculating the perimeter and area of a regular hexagon is known as the hexagon formula.
Read More: Hexagon
The hexagon formula for a hexagon with side length s is as follows :
Area of Hexagon
The formula for the Area of the Hexagon is
Area = (3√3s2)/2
Where s is the side of the hexagon
Perimeter of Hexagon
The formula for Perimeter of a Hexagon is
Perimeter = 6s
Where s is the side of Hexagon
Solved Problems on Hexagon
Problem 1: Calculate the perimeter and area of a regular hexagon having a side equal to 5 units.
Solution:
To Find : Perimeter and Area
Given : s = 5 units.
Using the hexagon formula for perimeterPerimeter(P) = 6s
P = 6 × 5
P = 30 unitsUsing the regular hexagon formula for Area
= (3√3s2 ) /
= {(3√3(5)2 }/ 2
= {(3√3 (25)} /
= (3 x 1.7320 x 25 ) / 2
= 129.9/ 2
= 64.95 sq. unitTherefore the perimeter of Hexagon is 30 units and area is 64.95 sq. units .
Problem 2: A hexagonal board thatthat has a perimeter of 18 inches. Find its area.
Solution:
To Find : Area of the hexagon.
Given : Perimeter = 18 inches.
The perimeter of hexagon = 6s
18 = 6 s
s = 18/6
= 3 inches.Using the hexagon formula for Area :
Area of hexagon
= {3√3(3)2}/2
= {3 x 1.7320 x 9}/ 2
= 46.764 / 2
= 23.382 sq. inches .therefore the Area of hexagonal board is 23.382 sq . inches .
Problem 3: Determine the side of the regular hexagon whose perimeter is 30 units.
Solution:
To Find : Side of hexagon = s
Given : perimeter = 30 units.
Using the hexagon formula for perimeter
Perimeter(P) of hexagon = 6s
30 = 6 × s
s = 30/6 units
= 5 unitshence the side of hexagon is 5 units .
Problem 4: What is the area of a regular hexagon whose side length is equal to 6 cm?
Solution:
As we know ;
Area of hexagon = (3√3 s2)/2Area = {3√3 (6)2 /2
Area = {3 × 1.7320 × 36}/2
= 187.056/ 2
= 93.52 sq . cmhence the area of hexagon is 93.52 sq . cm
Problem 5: Determine the side of the regular hexagon whose perimeter is 72 units.
Solution:
To Find : Side of hexagon = s
Given : perimeter = 72 units.
Using the hexagon formula for perimeter
Perimeter(P) of hexagon = 6s
72 = 6 × s
s = 72/6 units
= 12 unitsHence, the side of hexagon is 12 units.
Problem 6: Calculate the perimeter and area of a regular hexagon having a side equal to 8 units.
Solution:
To Find: Perimeter and Area
Given: s = 8 units.
Using the hexagon formula for perimeter
Perimeter(P) = 6s
P = 6 × 8
P = 48 unitsUsing the regular hexagon formula for Area
= (3√3s²) / 2
= {(3√3(8)²} / 2
= {(3√3 (64)} / 2
= (3 x 1.7320 x 64) / 2
= 332.928 / 2
= 166.464 sq. unitsTherefore the perimeter of Hexagon is 48 units and area is 166.464 sq. units.
Problem 7: A hexagonal board that has a perimeter of 24 inches. Find its area.
Solution:
To Find: Area of the hexagon.
Given: Perimeter = 24 inches.
The perimeter of hexagon = 6s
24 = 6 s
s = 24/6
= 4 inches.Using the hexagon formula for Area:
Area of hexagon
= {3√3(4)² }/2
= {3 x 1.7320 x 16}/2
= 83.136 / 2
= 41.568 sq. inchesTherefore the Area of hexagonal board is 41.568 sq. inches.
Problem 8: Determine the side of the regular hexagon whose perimeter is 54 units.
Solution:
To Find: Side of hexagon = s
Given: perimeter = 54 units.
Using the hexagon formula for perimeter
Perimeter(P) of hexagon = 6s
54 = 6 × s
s = 54/6 units
= 9 unitsHence the side of hexagon is 9 units.
Problem 9: What is the area of a regular hexagon whose side length is equal to 7 cm?
Solution:
As we know;
Area of hexagon = (3√3 s²)/2
Area = {3√3 (7)² /2
Area = {3 × 1.7320 × 49} / 2= 254.34 / 2
= 127.17 sq. cmHence the area of hexagon is 127.17 sq. cm.
Problem 10: Determine the side of the regular hexagon whose perimeter is 60 units.
Solution:
To Find: Side of hexagon = s
Given: perimeter = 60 units.
Using the hexagon formula for perimeterPerimeter(P) of hexagon = 6s
60 = 6 × s
s = 60/6 units
= 10 unitsHence, the side of hexagon is 10 units.