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Heron's Formula

Heron's formula (sometimes called Hero's formula) gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin.

The semiperimeter equals half the sum of the sides. The area equals the square root of the product of the semiperimeter and the differences between the semiperimeter and each side.

Formula

{QuantityVariable["s", "Length"] == (QuantityVariable["a", "Length"] + QuantityVariable["b", "Length"] + QuantityVariable["c", "Length"])/2, QuantityVariable["A", "Area"] == Sqrt[QuantityVariable["s", "Length"]*(-QuantityVariable["a", "Length"] + QuantityVariable["s", "Length"])*(-QuantityVariable["b", "Length"] + QuantityVariable["s", "Length"])*(-QuantityVariable["c", "Length"] + QuantityVariable["s", "Length"])]}

symbol description physical quantity
s semiperimeter "Length"
a first side length "Length"
b second side length "Length"
c third side length "Length"
A area "Area"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Heron's Formula"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Heron's Formula"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Heron's Formula"], {QuantityVariable["s","Length"] -> None, QuantityVariable["A","Area"] -> 10}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 60

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