Triangle Area Calculator
Calculate triangle area using base & height or Heron's formula.
Area uses square units.
Base can be any side with a matching perpendicular height.
Height must be perpendicular to the base.
Triangle area
30 square units
Space inside the triangle.
Formula used
Area = 1/2 × base × height
Area = 1/2 × 10 × 6
Method
Base and height
Unit display
square units
Semi-perimeter
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Perimeter
—
Triangle type
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Validity note
Valid base-height calculation.
Triangle Area Formulas
Base and Height
Area = 1/2 × base × height
Right Triangle
Area = 1/2 × leg₁ × leg₂
Heron’s Formula
s = (a + b + c) ÷ 2; Area = √(s(s − a)(s − b)(s − c))
Two Sides and Included Angle
Area = 1/2 × a × b × sin(C)
Equilateral Triangle
Area = (√3 ÷ 4) × side²
Variable Explanations
base
Side chosen as the bottom or reference side.
height
Perpendicular distance from base to opposite vertex.
a, b, c
Triangle side lengths.
s
Semi-perimeter, or half the perimeter.
C
Included angle between two known sides.
sin(C)
Sine of the included angle.
square units
Units used for area.
Triangle Diagram and Visual Explanation
Height must meet the chosen base at a right angle. The base can be any side if the matching perpendicular height is known. Area measures the region inside the triangle.
Worked Examples
Base 10 and height 6
Formula: Area = 1/2 × base × height
Substitution: 1/2 × 10 × 6
Answer: 30 square units
Base and height must be perpendicular.
Right triangle legs 3 and 4
Formula: Area = 1/2 × leg₁ × leg₂
Substitution: 1/2 × 3 × 4
Answer: 6 square units
The two legs meet at a right angle.
Sides 3, 4, and 5
Formula: Heron’s formula
Substitution: s = 6; Area = √(6×3×2×1)
Answer: 6 square units
This is a 3-4-5 right triangle.
Sides 7, 8, and 9
Formula: Heron’s formula
Substitution: s = 12; Area = √(12×5×4×3)
Answer: ≈ 26.83 square units
Heron’s formula works when all three sides are known.
Sides 8 and 10 with included angle 30°
Formula: Area = 1/2 × a × b × sin(C)
Substitution: 1/2 × 8 × 10 × sin(30°)
Answer: 20 square units
The angle must be between the two known sides.
Equilateral side 8
Formula: Area = (√3 ÷ 4) × side²
Substitution: (√3 ÷ 4) × 8²
Answer: ≈ 27.71 square units
All sides are equal.
Invalid sides 1, 2, and 5
Formula: Triangle inequality
Substitution: 1 + 2 is not greater than 5
Answer: Invalid
These side lengths cannot form a triangle.
Base 12 cm and height 5 cm
Formula: Area = 1/2 × base × height
Substitution: 1/2 × 12 × 5
Answer: 30 cm²
Area uses square units.
Base-Height, Heron’s Formula, and Trigonometry Methods
Base-height
Best when a perpendicular height is known.
Heron’s formula
Useful when all three sides are known.
Trigonometry
Useful when two sides and the included angle are known.
Right triangle
Uses the two legs directly.
Equilateral shortcut
Uses one side length because all sides are equal.
Validation
Side lengths must be positive and form a real triangle.
Common Triangle Types and Use Cases
Common Triangle Area Mistakes
Understanding Your Result
Area
Space inside the triangle.
Base-height result
Half the rectangle or parallelogram formed by base and height.
Heron’s result
Area calculated from three side lengths.
Semi-perimeter
Half of the triangle perimeter.
Included angle result
Area based on two sides and the angle between them.
Triangle validity
Whether the entered values can form a real triangle.
Frequently Asked Questions
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