How to Find Area of a Triangle

Calculating the area of a triangle is easy once you know the triangle area formula. Whether you have a right triangle, an equilateral triangle, or a scalene triangle, simple steps will help you calculate triangle area accurately every time.

What Is a Triangle?

A triangle is a three-sided shape in geometry. It has:

• Three sides (a, b, c)
• Three angles (A, B, C)
• A base (b) and a height (h) you can use to find its area

There are three main types of triangles:

• Equilateral triangle: All sides equal
• Isosceles triangle: Two sides equal
• Scalene triangle: All sides different

Key Components of a Triangle

• Base (b): Any side you choose as the bottom.
• Height (h): Perpendicular distance from the base to the opposite vertex.
• Side lengths (a, b, c): Used in special formulas like Heron’s.
• Angles (A, B, C): Used when you know two sides and the included angle.

The Basic Triangle Area Formula

The most common formula for triangle area is:

Area=12×b×hArea=21×b×h

• b = base
• h = height

This area formula works for any triangle when you know its base and height.

How to Find the Height of a Triangle

• Direct measurement: Drop a straight line (altitude) from the top vertex to the base.
• Right triangles: Use the two legs as base and height.
• Scalene triangles: Draw the altitude and use the Pythagorean theorem if needed.

Alternate Area Formulas

When you don’t know the height, use these formulas:

1. Heron’s formula (for any triangle):
   Let s=a+b+c2s=2a+b+c. Then
   Area=s(s−a)(s−b)(s−c)Area=s(s−a)(s−b)(s−c)
2. Two sides and included angle:
   If you know sides a and b and angle C between them:
   Area=12×a×b×sin⁡(C)Area=21×a×b×sin(C)

Worked Examples

Right Triangle Example

• a = 6, b = 8 (legs)
• Area = ½ × 6 × 8 = 24

Equilateral Triangle Example

• a = 5
• Height = 52−(2.5)2=4.3352−(2.5)2=4.33
• Area = ½ × 5 × 4.33 = 10.83

Scalene Triangle with Heron’s Formula

• a = 7, b = 8, c = 9
• s = (7 + 8 + 9) / 2 = 12
• Area = √[12 × 5 × 4 × 3] = √720 = 26.83

Common Mistakes to Avoid

• Mixing up base and height. The height must be perpendicular.
• Forgetting to halve (b×h)(b×h).
• Plugging wrong side lengths into Heron’s formula.

Practice Problems

1. b = 10, h = 6 → Area = 30
2. a = 9, b = 12, c = 15 (use Heron’s)
3. a = 4, b = 7, angle C = 60° → Area = ½ × 4 × 7 × sin(60°) = 12.12

FAQs

Can you find area without knowing the height?
Yes—use Heron’s formula or the two-sides-and-angle formula.

What units are used for triangle area?
Square units, like cm², m², or in².

How do I convert triangle area into different units?
Convert all measurements (base and height or sides) into the same unit before calculating.

Read More: How to Find Area of a Trapezoid: Formula, Examples & Step-by-Step Guide