Triangle Area

Right Angled Triangle

A right-angled triangle has one angle equal to 90°. The area is:

△ = ½ × b × h

Equilateral Triangle

All sides equal, all angles 60°. Area:

△ = (√3 / 4) × a²

Isosceles Triangle

Two equal sides. Area:

△ = (a/4) × √(4b² − a²)

Heron's Formula

For triangle with sides a, b, c and semi-perimeter s = (a+b+c)/2:

△ = √[s(s−a)(s−b)(s−c)]

Area of Triangle: Summary

Properties	Area Formula	Remarks
Base and Height	△ = ½ bh	b = base, h = height
Three sides	△ = √[s(s−a)(s−b)(s−c)]	s = (a+b+c)/2
Two sides and included angle	△ = ½ bc sin A	A between sides b and c
Equilateral Triangle	△ = (a²√3)/4	a = side length
Three Vertices (x₁,y₁), etc.	△ = ½ |det|	Determinant form
Two co-initial vectors	△ = ½ |a × b|	Cross product magnitude