# 9th Class Mathematics Heron's Formula

Heron's Formula

Category : 9th Class

Heron's Formula

• Area of a triangle $=\frac{1}{2}\times \operatorname{base}\,\times \,height$

• Area of a right angled isosceles triangle with perpendicular sides each equal to 'a' units$=\frac{1}{2}{{a}^{2}}$ sq. Units.

• Heron's formula:

Area of a triangle $=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$where a, b, c are the sides of the triangle and

s = semi perimeter i.e., half the perimeter of the triangle =$=\frac{a+b\text{ }+c}{2}$

Note: Heron's formula can be used when three sides of triangle are given and can be applied to any triangle.

• Area of an equilateral triangle with each side equal to 'a' units $=\frac{\sqrt{3}}{4}{{a}^{2}}$sq. units.
• Area of an equilateral triangle$=\frac{{{h}^{3}}}{\sqrt{3}}$sq. units where altitude$h=\frac{\sqrt{3}}{2}a$ units.
• Area of a quadrilateral whose sides and one diagonal are given, can be calculated by dividing the quadrilateral into two triangles and using the Heron's formula.

• Three positive integers a, b and c such that is${{c}^{2}}={{a}^{2}}+{{b}^{2}}$ called a Pythagorean triplet.

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##### Notes - Herons Formula

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