Heron’s formula and its application

heron's formula

What do you understand by using the formula of hero or heroon?

Heron’s formula in geometry is a formula for finding the area of a triangle when all three sides are known. It is also called ‘Hero’s formula’. The sutra is named after Heron of Alexandria.

Formula of heron

heron's formula class 9
heron’s formula class 9

Δ=√s(s-a)(s-b)(s-c)

s= a+b+c/2

a + b + c / 2 is called half-finite.The half-finite is denoted s.

a + b + c is called the perimeter of triangle ABC.

Where AB = c, BC = a, CA = b

Perimeter of triangle = Sum of the three sides (a + b + c)

Another method of finding the area of a triangle

Area of triangle = 1/2 × base × corresponding height.

When AC = b and BD = h where BD⊥AC then

heron's formula class 9

Area of triangle = ½ × bh

What is Pythagoras theorem?

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then which is the right angle in front of the first arm.

heron's formula class 9

Hypotenuse = perpendicular ² + base²

Hence, there is a right angle.

Area of right triangle = 1/2 × base × corresponding height

Area of equilateral triangle = √3 / 4 × side²

Area of the parallelogram = base × height.

Perimeter of parallelogram = 2 (sum of adjacent sides)

Area of rhombus = ½ × (product of diagonals)

Perimeter of rhombus = 4 × side

Area of a quadrilateral = ½ × (sum of vertices facing the corresponding vertices).

Area of trapezium = (sum of parallel sides) × height.

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