Mensuration

Chapter: Mensuration (क्षेत्रमिति)

Mensuration is the branch of mathematics that deals with the study of geometric shapes, their areas, and their perimeter/boundary lengths.
Closed Figure: A figure that starts and ends at the same point with no breaks (e.g., a circle, square, triangle).

Definition: The continuous line forming the boundary of a closed geometric figure. In simple terms, it is the total distance around the outside of a shape.
Unit: Measured in linear units like centimeters ($cm$), meters ($m$), kilometers ($km$), etc.

Perimeter of a Rectangle (आयत का परिमाप): Perimeter = 2 × (Length + Breadth) P = 2 × (l + b) (where $l$ = length, $b$ = breadth)
Perimeter of a Square (वर्ग का परिमाप): Perimeter = 4 × Side P = 4 × a (where $a$ = length of each side)
Perimeter of an Equilateral Triangle (समबाहु त्रिभुज का परिमाप): Perimeter = 3 × Side P = 3 × a
Perimeter of any Regular Polygon (समबहुभुज का परिमाप): Perimeter = Number of sides × Length of each side

Definition: The amount of surface enclosed within a closed geometric figure.
Unit: Measured in square units like square centimeters ($cm^2$), square meters ($m^2$), etc.

Area of a Rectangle (आयत का क्षेत्रफल): Area = Length × Breadth A = l × b
Area of a Square (वर्ग का क्षेत्रफल): Area = Side × Side A = a × a or a^2

$1 \text{ meter (m)} = 100 \text{ centimeters (cm)}$
$1 \text{ kilometer (km)} = 1000 \text{ meters (m)}$
$1 \text{ square meter (m}^2\text{)} = 100 \text{ cm} \times 100 \text{ cm} = 10,000 \text{ cm}^2$

Always write units: Do not forget to write units (like $\text{cm}$, $\text{m}^2$, etc.) in your final answer.
Same Units Rule: Before calculating the perimeter or area, ensure all dimensions are in the same unit (convert $m$ to $cm$ or vice versa if needed).
Difference between Perimeter and Area:
- Use Perimeter when finding the length of wire, fencing, or running around a field.
- Use Area when carpeting a room, painting a wall, or covering a surface with tiles.