Question
Find the area of a regular hexagon whose side measures $14\sqrt{3}$ cm.
The correct answer is
$882\sqrt{3} cm^2$
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$^2$.
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Important Questions from Mensuration 2D (Notes)
- A 2 cm wide wooden strip is to be fixed on a photo of 40 cm x 30 cm size all along its four sides. What is the minimum length of the wooden strip required?
- $110$ मी. $\times 60$ मी. घास-आच्छादित आयताकार प्लॉट के अंदर चारों ओर $2$ मी. चौड़ा बजरी का रास्ता बनाना है। $₹2$ प्रति वर्ग मी. की दर से बजरी बिछाने का लागत ज्ञात कीजिए।
- The perimeter of a square is $596$ m. Its area (in m$^2$) is:
- A hollow spherical shell is made of a metal of density 4 g/cm$^3$. Its internal and external radius are 15 cm and 18 cm, respectively. What is the weight (in kg) of the shell?
(Use $\pi = \frac{22}{7}$ and Density = $\frac{\text{Mass}}{\text{Volume}}$) - Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 4 metres per second into a cylindrical tank, the radius of whose base is 80 cm. By how much will the level of water rise in 16 minutes?
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