Mensuration Formulas and Theorems

Definition and Importance

• Mensuration is the branch of mathematics that deals with the measurement of geometric shapes, including their perimeter, area, and volume.
• It is an essential concept in mathematics, physics, engineering, and other fields, as it helps in solving problems involving sizes and shapes of objects.

Perimeter and Circumference

• Perimeter: The distance around a two-dimensional shape, calculated by adding the lengths of all its sides.
• Circumference: The distance around a circle, calculated using the formula: Circumference = 2 × π × radius.

Area

• Area of a rectangle: length × width
• Area of a triangle: (base × height) / 2
• Area of a circle: π × radius^2
• Area of a parallelogram: base × height
• Area of a trapezium: (sum of parallel sides) × height / 2

Volume

• Volume of a rectangular prism: length × width × height
• Volume of a cylinder: π × radius^2 × height
• Volume of a sphere: (4/3) × π × radius^3

Surface Area

• Surface area of a rectangular prism: 2 × (length × width + width × height + height × length)
• Surface area of a sphere: 4 × π × radius^2
• Surface area of a cylinder: 2 × π × radius × (radius + height)

Formulas and Theorems

• Pythagorean theorem: a^2 + b^2 = c^2 (for right-angled triangles)
• Heron's formula: area of a triangle = √(s(s-a)(s-b)(s-c)) (where s is the semi-perimeter)
• Brahmagupta's formula: area of a cyclic quadrilateral = √(s(s-a)(s-b)(s-c)(s-d)) (where s is the semi-perimeter)