Regular Hexagon Area Practice Problems & Calculation Worksheets

Master regular hexagon area formulas with step-by-step practice problems. Calculate hexagon areas from side length, perimeter, and more advanced polygon exercises.

📚Master Regular Hexagon Area Calculations

Apply the formula A = (6a²√3)/4 to calculate hexagon areas from side lengths
Find side lengths when given the hexagon area using inverse calculations
Calculate hexagon areas from perimeter measurements by finding individual sides
Solve complex problems involving hexagons with radical expressions and square roots
Work with advanced hexagon problems using algebraic manipulation and equation solving
Master the relationship between hexagon sides, angles, and area properties

Understanding Regular polygons - Advanced

Complete explanation with examples

Calculation of the Area of a Regular Hexagon - Let's Calculate It This Way!

The regular hexagon belongs to the family of regular polygons. It is a polygon in which all sides, and all angles, are equal to each other. By its name, we can understand that it is a geometric figure with $6$ different sides. The sum of its internal angles equals $720^o$ degrees. Therefore:

external angle $=60^o$ ; internal angle $=120^o$

Detailed explanation

Practice Regular polygons - Advanced

Test your knowledge with 4 quizzes

A hexagon has a perimeter of 72 cm.

Calculate the area of the hexagon.

Examples with solutions for Regular polygons - Advanced

Step-by-step solutions included

Exercise #1

Below is a hexagon that contains a rectangle inside it.

The area of the rectangle is 28 cm².

What is the area of the hexagon?

Step-by-Step Solution

Since we are given the area of the rectangle, let's first work out the length of the missing side:

$7\times a=28$

We'll now divide both sides by 7 to get:

$a=4$

Since all sides are equal in a hexagon, each side is equal to 4.

Now let's calculate the area of the hexagon:

$\frac{6\times a^2\times\sqrt{3}}{4}$

$\frac{6\times4^2\times\sqrt{3}}{4}$

Finally, we simplify the exponent in the denominator of the fraction to get:

$6\times4\times\sqrt{3}=24\times\sqrt{3}=41.56$

Answer:

41.56

Video Solution

Exercise #2

Given the hexagon in the drawing:

What is the area?

Step-by-Step Solution

Answer:

64.95

Video Solution

Exercise #3

Given the hexagon in the drawing:

What is the area?

Step-by-Step Solution

Answer:

166.27

Video Solution

Exercise #4

Given the hexagon in the drawing:

What is the area?

Step-by-Step Solution

Answer:

41.56

Video Solution

Exercise #5

A hexagon has a sides measuring 5 cm.

What is the area of the hexagon?

Step-by-Step Solution

Answer:

64.95 cm²

Video Solution

Frequently Asked Questions

Everything you need to know about Regular polygons - Advanced

What is the formula for calculating the area of a regular hexagon?

The area of a regular hexagon is A = (6a²√3)/4, where 'a' is the length of one side. This formula works because a regular hexagon can be divided into 6 congruent equilateral triangles, each with area (a²√3)/4.

How do you find the side length of a hexagon when given the area?

To find the side length from area, rearrange the formula: a = √(4A/(6√3)). First multiply the area by 4, then divide by 6√3, and finally take the square root of the result.

What are the interior and exterior angles of a regular hexagon?

A regular hexagon has interior angles of 120° and exterior angles of 60°. The sum of all interior angles is 720°, which equals (6-2) × 180°.

How do you calculate hexagon area from perimeter?

Steps to find area from perimeter: 1) Divide perimeter by 6 to get side length, 2) Apply the area formula A = (6a²√3)/4, 3) Substitute the side length and calculate.

Why does a regular hexagon divide into 6 triangles?

Drawing lines from the center to each vertex creates 6 congruent isosceles triangles. Each triangle has a central angle of 60°, making them equilateral triangles with area (a²√3)/4.

What makes hexagon area problems challenging for students?

Common challenges include: working with square roots and radicals, rearranging the area formula to solve for side length, converting between different given measurements (perimeter vs. side), and managing algebraic manipulation in complex problems.

How do you solve hexagon problems with radical expressions?

When areas involve radicals like (√3)³: 1) Simplify the radical expression first, 2) Set up the equation A = (6a²√3)/4, 3) Solve algebraically by isolating a², 4) Take the square root to find the side length.

What real-world applications use regular hexagon area calculations?

Hexagon areas are used in: architecture and tile design, engineering for bolt patterns and structural elements, biology for honeycomb cell calculations, and manufacturing for hexagonal nuts and fasteners.

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