Power Calculators

📏 Triangle Area from Median Calculator

Calculate triangle area when one side, the adjacent side and the median to the known base are given. Uses the median geometry and Pythagorean relationship.

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Enter details

The median is drawn to this base.
Use one of the two sides meeting at the median vertex.
Triangle Area
29.3939
Perpendicular Height
5.87878
Valid Geometry
1

Also available in our Android app, with charts and full breakdown tables.

📘 About the Median Area

A median joins a vertex to the midpoint of the opposite side.

This calculator uses the base, one adjacent side and the median drawn to that base.

The calculation first finds the offset from the base midpoint and then derives the perpendicular height.

🧮 Formula

Offset from midpoint
x = (b²+a²/4-ma²)/a
Perpendicular height
h = √(b²-x²)
Triangle area
A = ah/2

Where

  • a = base
  • b = adjacent side
  • ma = median to base a
  • x = offset from the base midpoint
  • h = perpendicular height
The entered measurements must describe a physically possible triangle.

✏️ Worked example

Base 10 cm, adjacent side 7 cm, median 6 cm

You enter
Base a10 cm
Adjacent Side b7 cm
Median to Base ma6 cm
You get
Triangle Area29.3939
Perpendicular Height5.87878
Valid Geometry1

The calculator derives the perpendicular height and then the triangle area.

Try this example →

🧭 How to use this calculator

What you enter

  • Base a (cm)The median is drawn to this base.
  • Adjacent Side b (cm)Use one of the two sides meeting at the median vertex.
  • Median to Base ma (cm)

What you get

  • Triangle Area
  • Perpendicular Height
  • Valid Geometry

💡 Important condition

  • The median entered must be the median to the entered base.
  • The measurements must satisfy the geometry of a real triangle.
  • A non-positive derived height means the measurements do not define a non-degenerate triangle.

❓ Frequently asked questions

What is a median of a triangle?

A median is a segment from a vertex to the midpoint of the opposite side.

Does the median always equal the height?

No. They are equal only in special symmetric cases, such as an isosceles triangle when the median is drawn to the base.

What inputs does this calculator need?

It needs the base, one adjacent side and the median to that base.

Is this an advanced triangle calculator?

Yes. It is intended mainly for geometry and competitive mathematics problems.