Math July 13, 2026 · 8 Min Read

Area of Triangle Calculator – Guide & Formulas

Calculate the area of any triangle using multiple formulas: Base & Height, Heron’s formula (three sides), or SAS (two sides and one angle).

Find the area of any triangle. This versatile tool supports calculation via Base & Height, Three Sides (Heron’s formula), or Two Sides with the Included Angle (SAS).

Key Takeaway

Use the free Area of Triangle Calculator to calculate the area of any triangle using multiple formulas: base & height, heron’s formula (three sides), or sas (two sides and one angle). Get instant results with step-by-step explanations.

How to Use the Area of Triangle Calculator

  1. Select your calculation method: Base & Height, Three Sides (Heron’s), or Two Sides & Angle (SAS).
  2. Input the required dimensions in the fields.
  3. Check the computed surface area, perimeter, and geometric details.

The Formula

Area = 0.5 * base * height | Heron's: sqrt(s*(s-a)*(s-b)*(s-c)) where s = semiperimeter

Variable Definitions

  • b, h: Base and height
  • a, b, c: The three side lengths
  • s: Semiperimeter: (a + b + c) / 2

Calculating Area with Three Sides 5, 6, and 7

A surveyor needs to find the acreage of a triangular plot of land with measured boundaries of 50 meters, 60 meters, and 70 meters.

  1. Step 1: Set three sides a = 50, b = 60, c = 70.
  2. Step 2: Calculate semiperimeter s = (50+60+70)/2 = 90.
  3. Step 3: Apply Heron’s formula: √[90 * (90-50) * (90-60) * (90-70)] = √[90 * 40 * 30 * 20].
  4. Step 4: Compute Area ≈ 1469.69 square meters.

Frequently Asked Questions

What is Heron’s formula used for?

Heron’s formula allows you to calculate the area of a triangle when you only know the lengths of all three sides, without needing to know any angles or altitude heights.

Can a triangle have sides of any length?

No. The Triangle Inequality Theorem states that the sum of the lengths of any two sides must always be strictly greater than the length of the remaining side (a + b > c).

What is the SAS formula for triangle area?

If you know two sides (a, b) and the included angle (C), the area is calculated using Area = 0.5 * a * b * sin(C).