Playing with Constructions – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash, tailored for Class 6 in Mathematics.
This one-pager compiles key formulas and equations from the Playing with Constructions chapter of Ganita Prakash. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Circumference of a Circle: C = 2πr
C represents circumference, r is the radius of the circle. This formula calculates the distance around a circle, essential for circular constructions.
Area of a Circle: A = πr²
A represents area, r is the radius. This formula gives the space inside a circle, useful for determining space usage in circular designs.
Area of a Triangle: A = 1/2 × base × height
A is the area, base is the length of the triangle's base, height is the perpendicular distance from the base to the apex. This formula is key in many geometric constructions.
Area of a Rectangle: A = length × width
A is area, length and width are the rectangle's dimensions. This formula is fundamental in constructing rectangles.
Area of a Square: A = side²
A is area, side is the length of one side of the square. Used in square constructions.
Perimeter of a Rectangle: P = 2(length + width)
P is perimeter, and it represents the total distance around a rectangle. Important for defining boundaries in construction.
Perimeter of a Square: P = 4 × side
P is perimeter, side is the length of one side. Useful to establish the total boundary length for squares.
Diagonal of a Rectangle: d = √(length² + width²)
d is diagonal, length and width are the dimensions of the rectangle. This formula helps find the distance across a rectangle.
Straight Line Distance: d = √((x₂ - x₁)² + (y₂ - y₁)²)
d is the distance between two points (x₁, y₁) and (x₂, y₂). Important for measuring distances in any constructions.
Angle Sum of a Triangle: ∠A + ∠B + ∠C = 180°
This states that the angles in any triangle add up to 180 degrees. Useful in triangle constructions.
Equations
Circle Equation: (x - h)² + (y - k)² = r²
This represents a circle with center (h, k) and radius r. It forms the foundation for circular constructions in coordinate geometry.
Pythagorean Theorem: a² + b² = c²
In a right triangle, a and b are the legs, and c is the hypotenuse. This theorem is crucial for right-angle constructions.
Slope of a Line: m = (y₂ - y₁)/(x₂ - x₁)
m represents the slope of a line passing through points (x₁, y₁) and (x₂, y₂). Important in defining linear constructions.
Distance Formula: d = √((x₂ - x₁)² + (y₂ - y₁)²)
Calculates distance between points (x₁, y₁) and (x₂, y₂). Essential for measuring the distance in geometric constructions.
Volume of a Rectangular Prism: V = length × width × height
V is the volume, crucial for three-dimensional construction problems.
Volume of a Cylinder: V = πr²h
V is volume, r is radius, h is height. Useful for constructions involving cylinders.
Area of Rhombus: A = (d₁ × d₂)/2
A is area, d₁ and d₂ are the diagonals of the rhombus. Important in specific geometrical design constructions.
Exterior Angle Theorem: Exterior Angle = Sum of Opposite Interior Angles
This theorem helps in understanding angle relationships in polygon constructions.
Sum of Interior Angles of a Polygon: (n - 2) × 180°
n is the number of sides in the polygon. Useful for determining angle measures in multi-sided constructions.
Equation of a Line: y = mx + b
m is slope and b is y-intercept. This linear equation defines geometric relationships between points in construction.
