The Baudhayana-Pythagoras Theorem – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash Part II, tailored for Class 8 in Mathematics.
This one-pager compiles key formulas and equations from the The Baudhayana-Pythagoras Theorem chapter of Ganita Prakash Part II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Area of Square: A = s²
A is the area (in square units) and s is the side length of the square. This formula calculates the area, essential for understanding space within geometric shapes.
Diagonal of Square: d = s√2
d is the diagonal length and s is the side length. This formula arises from the properties of a right triangle formed by the sides of the square.
Baudhayana-Pythagorean Theorem: a² + b² = c²
In a right triangle, a and b are the lengths of the legs, and c is the hypotenuse. This theorem is fundamental for determining relationships between the sides of triangles.
Hypotenuse of Isosceles Right Triangle: c = a√2
c is the hypotenuse, and a is the length of equal sides. This formula shows how to find the hypotenuse in an isosceles right triangle context.
Area of Right Triangle: A = (1/2)ab
A is the area, and a and b are the lengths of the two perpendicular sides. This formula is commonly used for area calculations in triangles.
Doubling a Square: D = s√2
D is the side length of the square with double the area, derived from constructing a square on the diagonal of the original square.
Halving a Square: s' = s/√2
s' is the side length of the square with half the area of the original. It shows how to find the new side length mathematically.
Pythagorean Triples: a² + b² = c² where a, b, c are integers
This represents integer solutions for the side lengths of right triangles, crucial in number theory and geometry.
Area of Combined Squares: A = A₁ + A₂ = a² + b²
A is the area of the combined square, A₁ and A₂ are the areas of the smaller squares with lengths a and b, respectively.
Length Relationship: c = √(a² + b²)
c is the hypotenuse of the triangle defined by legs a and b. This calculation is used fundamentally to solve for unknown sides.
Equations
c² = 2a² (for Isosceles Right Triangle)
c is hypotenuse, and a are the lengths of equal sides. This relates the hypotenuse to the other sides of the triangle.
3² + 4² = 5²
This specific case of the Pythagorean theorem demonstrates the relationship between the sides of a right triangle.
A = 1/2 × b × h
This equation gives the area (A) of a triangle based on the base (b) and height (h), useful for triangular area calculations.
c = √(α² + β²)
c represents the hypotenuse in terms of any two sides α and β of a right triangle, fundamental in geometry.
s' = s × 1/√2
This relates the original square side length (s) to a new side length (s') of a smaller square, showing overlap in relationships with areas.
D² = a² + b² (Combined area)
D represents the diagonal square when constructed from two squares of areas a² and b².
4 + 12 = c²
This represents another example using values for a right triangle which involves finding that hypotenuse.
x² + y² = 13²
This uses the Pythagorean Theorem with specific integers showing if both x and y fulfill the theorem regarding a triangle.
A_total = A₁ + A₂ + A₃...
Used when multiple areas combine in geometric constructions, A_total gives a total area for all shapes together.
9 = 2x + 1
An equation derived from the lotus stem problem to find the depth of the lake based on the properties of triangles.
