Know the Mensuration Formulas of Different Figures

we will tell you what Mensuration Formulas are. If you don't know Mensuration Formulas, you can read this article because today we will talk about Mensuration Formulas in this article.

In mathematical geometry, the formula for area is of utmost importance. According to a mathematical survey, more than 45% of questions related to all types of examinations (competitive, board, government, or non-government) in Hindi are related to all area formulas. Therefore, it is essential to use a specific formula to solve such questions.

In recent years, it has been observed in board and competitive exams that more questions related to geometric figures such as cone, cylinder, sphere, rectangle, triangle, quadrilateral, etc., have been asked. This indicates how important it is to remember the area formulas.

According to the requirement, a detailed study of almost all the components related to area such as volume, area, perimeter, etc., will be done here. This will not only help in solving questions but also strengthen your grip on mathematics.

Definition of Area

Geometric mensuration is a branch of mathematics that fulfills measurement-related activities. Even in measurement, it is specifically related to the origin and use of formulas and their applications for area, volume, and geometric figures.

Perimeter: In mensuration, perimeter or circumference is a distance that forms closed figures along with line segments. In other words, the sum of all the sides of a figure is its perimeter or circumscribed figure.

Area: The measure of a two-dimensional figure's quantity is called area. The area whose measurement is to be determined is usually enclosed by a closed curve. The area is always measured in square units.

Volume: The space enclosed by a three-dimensional figure is called volume. The enclosed space by an object is expressed in terms of length, width, and height. Volume is always measured in cubic units.

All Formulas of Mensuration

The formulas of two-dimensional figures such as rectangle, square, right triangle, isosceles triangle, etc., include the area and perimeter, as well as three-dimensional figures such as cube, cylinder, cone, sphere, etc., include volume, area, and perimeter. Details are here, which will lead you towards a bright future in mathematics.

Formula for Square

• Perimeter of a square = 4 × side
• Diagonal of a square = side × √2 = side × √2
• Diagonal of a square = √2 × area of the square
• Area of a square = (side × side) = side²
• And side = √area
• Area of a square = ½ × (product of diagonals) = ½ × d²

Formula for Rectangle

• Perimeter of a rectangle = 2(length + width)
• Area of a rectangle = length × width
• Diagonal of a rectangle = √(length² + width²)

Formula for Rhombus

• Area of a rhombus = ½ (product of diagonals)
• In other words, A = (d1 × d2)/2 square units
• Perimeter of a rhombus = 4 × side
• In a rhombus, (AC)² + (BD)² = 4a²

Formula for Circle

• Angle A + Angle C = 180°
• Angle B + Angle D = 180°
• Area = √[s(s-a) (s-b) (s – c)]
• Perimeter, S = ½ (a + b + c + d)

Formula for Regular Polygon

• Perimeter of a regular polygon = number of sides × length of one side
• Area of a regular hexagon = 6 × ¼√3 (side)²
• Each interior angle of an n-sided regular polygon = (2n – 4) × 90°.

Formula for Triangle

• Perimeter of a triangle = sum of all three sides
• Area of a triangle = ½ × base × height
• Area of a triangle = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter and a, b, c are the lengths of the sides.

Formula for Right Triangle

• Area of a right triangle = ½ × base × height
• Hypotenuse of a right triangle = √(base² + height²)

Formula for Equilateral Triangle

• Perimeter of an equilateral triangle = 3 × side
• Area of an equilateral triangle = (√3/4) × side²

Formula for Isosceles Triangle

• Perimeter of an isosceles triangle = 2 × side + base
• Area of an isosceles triangle = ½ × base × height

Formula for Quadrilateral

Perimeter of a quadrilateral = sum of all four sides

Area of a quadrilateral can be calculated using different formulas depending on the type of quadrilateral (e.g., square, rectangle, parallelogram, trapezium, etc.)

Formula for Circle

• Circumference of a circle = 2πr, where r is the radius
• Area of a circle = πr², where r is the radius
• Diameter of a circle = 2r

Formula for Cylinder

• Curved surface area of a cylinder = 2πrh, where r is the radius and h is the height
• Total surface area of a cylinder = 2πr(r + h)
• Volume of a cylinder = πr²h

Formula for Cone

• Curved surface area of a cone = πrl, where r is the radius and l is the slant height
• Total surface area of a cone = πr(r + l), where r is the radius and l is the slant height
• Volume of a cone = (1/3)πr²h, where r is the radius and h is the height

Formula for Sphere

• Surface area of a sphere = 4πr², where r is the radius
• Volume of a sphere = (4/3)πr³, where r is the radius

These are some of the basic formulas used in mensuration. It's important to understand and remember these formulas to solve problems related to geometric figures.

Formula for Square

• Perimeter of a square = 4 × side
• Area of a square = side²
• Diagonal of a square = side × √2

Formula for Rectangle

• Perimeter of a rectangle = 2 × (length + width)
• Area of a rectangle = length × width
• Diagonal of a rectangle = √(length² + width²)

Formula for Parallelogram

• Perimeter of a parallelogram = 2 × (side₁ + side₂)
• Area of a parallelogram = base × height

Formula for Trapezium

• Perimeter of a trapezium = sum of all four sides
• Area of a trapezium = (1/2) × (sum of parallel sides) × height

Formula for Regular Polygon

• Perimeter of a regular polygon = number of sides × length of each side
• Interior angle of a regular polygon = [(number of sides - 2) × 180°] / number of sides
• Exterior angle of a regular polygon = 360° / number of sides

Formula for Cuboid

• Surface area of a cuboid = 2 × (length × width + width × height + height × length)
• Volume of a cuboid = length × width × height
• Diagonal of a cuboid = √(length² + width² + height²)

Formula for Prism

• Surface area of a prism = 2 × base area + lateral area
• Volume of a prism = base area × height

Formula for Pyramid

• Surface area of a pyramid = base area + (1/2) × perimeter of base × slant height
• Volume of a pyramid = (1/3) × base area × height

Formula for Ellipse

• Perimeter of an ellipse = 2π√((a² + b²)/2), where a and b are the semi-major and semi-minor axes respectively
• Area of an ellipse = πab, where a and b are the semi-major and semi-minor axes respectively

Conclusion

These are some additional formulas that can be used in various mensuration problems. Remembering and applying these formulas correctly will help in solving geometric calculations and measurements accurately.