Perimeter and Area of Regular Hexagon

Here we will discuss about the perimeter and area of a Regular hexagon and some example problems.

$Perimeter and Area of Regular Hexagon$

Perimeter (P) = 6 × side = 6a

Area (A) = 6 × (area of the equilateral ∆OPQ)

= 6 × $\frac{√3}{4}$ a$^{2}$

= $\frac{3√3}{2}$ a$^{2}$

If the area of a regular hexagon is 24√3 cm², find its perimeter.

Solution:

Let the side of a regular hexagon be a.

Then, its area = $\frac{3√3}{2}$ × (Side)²

= $\frac{3√3}{2}$ × a²

Therefore, 24√3 cm² = $\frac{3√3}{2}$ × a²

⟹ a² = $\frac{48√3}{3√3}$ cm²

⟹ a² = 16

⟹ Therefore, a ⟹ 4 cm.

Therefore, perimeter = 6a = 6 × 4 cm = 24 cm.

You might like these

$Here we will solve different types of problems on finding the area and perimeter of combined figures. 1. Find the area of the shaded region in which PQR is an equilateral triangle of side 7√3 cm. O is the centre of the circle. (Use π = $\frac{22}{7}$ and √3 = 1.732.)$

Area and Perimeter of Combined Figures | Circle | Triangle |Square
Here we will solve different types of problems on finding the area and perimeter of combined figures. 1. Find the area of the shaded region in which PQR is an equilateral triangle of side 7√3 cm. O is the centre of the circle. (Use π = $\frac{22}{7}$ and √3 = 1.732.)
$Here we will discuss about the area and perimeter of a semicircle with some example problems. Area of a semicircle = $\frac{1}{2}$ πr$^{2}$ Perimeter of a semicircle = (π + 2)r. Solved example problems on finding the area and perimeter of a semicircle$

Area and Perimeter of a Semicircle | Solved Example Problems | Diagram
Here we will discuss about the area and perimeter of a semicircle with some example problems. Area of a semicircle = $\frac{1}{2}$ πr$^{2}$ Perimeter of a semicircle = (π + 2)r. Solved example problems on finding the area and perimeter of a semicircle
Area of a Circular Ring | Radius of the Outer Circle and Inner Circle
Here we will discuss about the area of a circular ring along with some example problems. The area of a circular ring bounded by two concentric circle of radii R and r (R > r) = area of the bigger circle – area of the smaller circle = πR^2 - πr^2 = π(R^2 - r^2)
Area and Circumference of a Circle |Area of a Circular Region |Diagram
Here we will discuss about the area and circumference (Perimeter) of a circle and some solved example problems. The area (A) of a circle or circular region is given by A = πr^2, where r is the radius and, by definition, π = circumference/diameter = 22/7 (approximately).
Perimeter and Area of Irregular Figures | Solved Example Problems
Here we will get the ideas how to solve the problems on finding the perimeter and area of irregular figures. The figure PQRSTU is a hexagon. PS is a diagonal and QY, RO, TX and UZ are the respective distances of the points Q, R, T and U from PS. If PS = 600 cm, QY = 140 cm