Utilnaro

Geometry formulas

Triangle area

Calculate triangle area from a base and perpendicular height or from three side lengths using Heron’s formula.

Formula

A=bh2 A = b × h / 2

Triangle area is one half of a chosen base multiplied by the perpendicular height to that base.

Triangle area calculator

Calculation method
What do you want to calculate?

Known values

The result updates automatically.

Triangle diagram
bhA ?
  • b · Base: known value
  • h · Height: known value
  • A · Area: value being calculated (?)

Result

10 m²

Substitution and calculation

A = b × h / 2 = 5 m × 4 m / 2 = 10 m²

Symbols and units

SymbolQuantitySISupported units
AareaArea enclosed by the triangle.m²m², cm², mm², km²
bbaseThe side selected as the base in the base-height formula.mm, cm, mm, km
hperpendicular heightPerpendicular distance from the opposite vertex to the line containing the base.mm, cm, mm, km
afirst sideFirst side used in Heron’s formula.mm, cm, mm, km
bsecond sideSecond side used in Heron’s formula.mm, cm, mm, km
cthird sideThird side used in Heron’s formula.mm, cm, mm, km

Formula rearrangements

Area from base and height

A = b × h / 2

Calculate the base

b = 2A / h

Calculate the height

h = 2A / b

Area from three sides

A = √(p(p-a)(p-b)(p-c))

Worked examples

Area from base and height

A triangle has a base of 10 cm and a perpendicular height of 6 cm. Find its area.

  1. 1Step 1: Use A = b × h / 2.
  2. 2Step 2: Multiply 10 cm by 6 cm to obtain 60 cm².
  3. 3Step 3: Divide by 2 to obtain 30 cm².

Result: 30 cm²

Area from three sides

A triangle has side lengths 13 cm, 14 cm, and 15 cm. Find its area using Heron’s formula.

  1. 1Step 1: Calculate the semiperimeter: p = (13 + 14 + 15) / 2 = 21 cm.
  2. 2Step 2: Substitute into Heron’s formula: A = √(21 × 8 × 7 × 6).
  3. 3Step 3: Take the square root of 7056 to obtain 84 cm².

Result: 84 cm²

Sources and review