Mathematical Theorems and Formulas for Class 6

1. The Pythagorean Theorem:
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

2. Area of a Rectangle:
The formula to calculate the area of a rectangle is given by multiplying its length by its width.
Area = Length × Width

3. Perimeter of a Rectangle:
The perimeter of a rectangle is the sum of all its sides. In the case of a rectangle, opposite sides are equal in length.
Perimeter = 2 × (Length + Width)

4. Area of a Triangle:
The formula to calculate the area of a triangle is given by multiplying its base by the height and then dividing the result by 2.
Area = (Base × Height) / 2

5. Perimeter of a Triangle:
The perimeter of a triangle is the sum of the lengths of its three sides.
Perimeter = Side1 + Side2 + Side3

6. Area of a Circle:
The formula to calculate the area of a circle is given by multiplying the square of its radius by the mathematical constant π (pi).
Area = π × (Radius)^2

7. Circumference of a Circle:
The circumference of a circle is the distance around its outer edge. It is calculated by multiplying the diameter of the circle by the mathematical constant π (pi).
Circumference = π × Diameter

8. Area of a Square:
The formula to calculate the area of a square is given by multiplying the length of one side by itself.
Area = Side × Side

9. Perimeter of a Square:
The perimeter of a square is the sum of the lengths of all its sides. In a square, all sides are equal in length.
Perimeter = 4 × Side

10. Volume of a Cuboid:
The volume of a cuboid can be calculated by multiplying its length, width, and height.
Volume = Length × Width × Height

These theorems and formulas are important for Class 6 students to understand and apply in various mathematical problems and calculations. They provide a foundation for further mathematical concepts and help in solving real-life problems related to shapes and measurements.