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Triangle Area Calculator

Triangle Area Calculator

Calculate triangle area using multiple methods: base × height, Heron's formula, or SAS (two sides and included angle). Get step-by-step solutions.

Triangle Area Calculator

Calculate triangle area using multiple mathematical methods. Choose the method based on your known values.

Calculation Method

Calculation Method:

Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
Results
Area Formulas
Base × Height:

Most basic method when height is known

Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
Heron's Formula:

When all three sides are known

Area=s(s−a)(s−b)(s−c)\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}
SAS Method:

Two sides and included angle

Area=12×a×b×sin⁡(C)\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)
Circumradius:

Using circumscribed circle

Area=abc4R\text{Area} = \frac{abc}{4R}
Inradius:

Using inscribed circle

Area=r×s\text{Area} = r \times s
When to Use Each Method
Base × Height:
  • When you know the base and perpendicular height
  • Simplest and most direct method
  • Common in basic geometry problems
Heron's Formula:
  • When all three side lengths are known
  • No angles required
  • Works for any triangle type
SAS Method:
  • Two sides and the included angle are known
  • Uses trigonometry
  • Common in physics and engineering
Circumradius:
  • Advanced geometry problems
  • When circumcircle is involved
  • Coordinate geometry applications
Inradius:
  • When incircle properties are known
  • Advanced triangle geometry
  • Competition mathematics

Calculation Methods

Base × Height

Classic formula using base and perpendicular height

A=12×b×hA = \frac{1}{2} \times b \times h

Heron's Formula

Calculate from three side lengths

A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}

SAS Method

Two sides and included angle

A=12absin⁡CA = \frac{1}{2}ab\sin C

Complete Triangle Area Formulas

Base × Height

A=12×base×heightA = \frac{1}{2} \times base \times height

Heron's Formula

A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}

where s = (a+b+c)/2

SAS Formula

A=12absin⁡CA = \frac{1}{2}ab\sin C

Circumradius Formula

A=abc4RA = \frac{abc}{4R}

Choosing the Right Method

Base × Height

Use when you know:

Any base and its perpendicular height

Heron's Formula

Use when you know:

All three side lengths (SSS)

SAS Formula

Use when you know:

Two sides and included angle

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