$882\sqrt{3} cm^2$
Area of Regular Hexagon
This section details the calculation for the area of a regular hexagon using its side length.
Hexagon Formula for Area
The area ($A$) of a regular hexagon with side length ($s$) is given by the formula:
$ A = \frac{3\sqrt{3}}{2} s^2 $
Steps to Calculate Area
Given: The side length $s = 14\sqrt{3}$ cm.
- Compute the square of the side length ($s^2$):
$ s^2 = (14\sqrt{3})^2 = 14^2 \times (\sqrt{3})^2 = 196 \times 3 = 588 $
- Substitute $s^2$ into the area formula:
$ A = \frac{3\sqrt{3}}{2} \times 588 $
- Simplify the expression:
$ A = 3\sqrt{3} \times \frac{588}{2} = 3\sqrt{3} \times 294 $
- Calculate the final area value:
$ A = (3 \times 294)\sqrt{3} = 882\sqrt{3} $
The area is $882\sqrt{3}$ cm$^2$.
Final Area Result
The calculated area of the regular hexagon is precisely $882\sqrt{3}$ cm$^2$.
Important Questions from Mensuration 2D (Notes)
- Find the area of a quadrilateral ABCD whose area is twice the area of a triangle PQR. The sides of triangle PQR are in the ratio 4:5:6 and the perimeter of the triangle is 90 cm (use $\sqrt{7} = 2.6$).
- Find the perimeter of the semi-circle of radius 21 cm.
$\left(\text{Take } \pi = \frac{22}{7}\right)$ - The length of a diagonal of a rectangular park is 25 meters, and that of one of its sides is 15 meters. Find the perimeter of the park.
- If the area of an equilateral triangle is given as $900 \text{ m}^2$, then what is its perimeter?
The difference between two parallel sides of a trapezium is 9 cm. The perpendicular distance between them is 52 cm. If the area of the trapezium is 988 \(cm^2\), find the lengths of the parallel sides (in cm).
