Triangle Area Calculator | Base×Height & Heron's | PanMaths
Calculate the area of any triangle using base & height or Heron's formula. Supports all triangle types with step-by-step solutions.
Base × Height Method
A = ½ × b × hMultiply base by height, then divide by 2. Height must be perpendicular to base.
Heron's Formula
A = √[s(s-a)(s-b)(s-c)]Where s = (a+b+c)/2 is the semi-perimeter. Works with just the three sides.
Two Sides + Included Angle
A = ½ × a × b × sin(C)Use when you know two sides and the angle between them.
Equilateral Triangle
A = (√3/4) × s²Special formula for equilateral triangles where all sides equal s.
Examples
Right Triangle: base 6, height 8
A = ½ × 6 × 8 = 24 square units = 24
Heron's: sides 3, 4, 5 (right triangle)
s = (3+4+5)/2 = 6. A = √[6×3×2×1] = √36 = 6 = 6
Equilateral: side 10
A = (√3/4) × 10² = (√3/4) × 100 ≈ 43.3 = ≈ 43.3
Scalene: sides 7, 8, 9
s = 12. A = √[12×5×4×3] = √720 ≈ 26.83 = ≈ 26.83
Frequently Asked Questions
What is the formula for the area of a triangle?
The most common formula is A = ½ × base × height. The base is any side, and the height is the perpendicular distance from the base to the opposite vertex.
How do I find the area with only 3 sides?
Use Heron's formula: First, find the semi-perimeter s = (a+b+c)/2. Then calculate A = √[s(s-a)(s-b)(s-c)]. This works for any valid triangle.
What makes sides invalid for a triangle?
The triangle inequality states that the sum of any two sides must be greater than the third. If a + b ≤ c (for any combination), no triangle can be formed.
Why is the area formula half base times height?
A triangle is exactly half of a parallelogram (or rectangle). If you duplicate a triangle and flip it, you get a parallelogram with area = base × height. Thus, triangle = ½ × base × height.
How do I find the height of a triangle?
If you know the area and base: h = 2A/b. For right triangles, one leg is the height. For others, you may need to draw the altitude from a vertex perpendicular to the opposite side.