Contents
Regular hexagon is a geometric figure; regular polygon with 6 equal angles and sides.
General formula for area calculation
The area (S) of a regular hexagon is calculated using the formula below, where a – the length of its side:
The formula is obtained as follows:
A regular hexagon consists of six equal equilateral triangles. The area of each is calculated as follows:
Therefore, the area of a regular hexagon is:
Area of a regular hexagon inscribed in a circle
The side of a regular hexagon is equal to the radius of the circle circumscribed around it (a=r).
This means that the area formula can be represented in this form (а replace with r):
Examples of tasks
Task 1
The side of a regular hexagon is 8 cm. Find its area.
Decision:
We use the first formula, in which the length of the side is involved:
Task 2
Calculate the area of a regular hexagon if the radius of a circle circumscribed around it is 15 cm.
Decision:
Let’s use the second formula (through the radius of the circle):
