Formulas & tables/Mathematics/Plane geometry/Area of an equilateral triangle

Area of an equilateral triangle

P=a234P=\dfrac{a^2\sqrt{3}}{4}

Result unit: area units

What it describes

The area of an equilateral triangle with side aa.

Symbols

PP
area
aa
side length

Where it comes from

A ready-made formula for the area of an equilateral triangle with side aa — it follows from the height h=a32h=\tfrac{a\sqrt3}{2}.

When to use it

An equilateral triangle (in hexagons, regular pyramids).

Example

The side of an equilateral triangle is a=4a=4. Find the area.
Substitutiona=4a=4.
ResultP=1634=43≈6.93P=\dfrac{16\sqrt3}{4}=4\sqrt3\approx6.93.

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