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Numbers · geometry · triangleArea of a triangle — formula and calculator

Work out the area of a triangle with the formula S = ½ × a × h — your numbers substituted and a diagram drawn. Units can be mixed, and the answer comes in the units you need, hectares and acres included.

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01Calculator02Formula03Example04Mistakes05Nearby06Related
01

Calculator

enter the sizes — the formula and diagram follow

Triangle

area · perimeter
a = 6 cmh = 4 cm
diagram · not to scale
What you know
The perimeter needs all three sides — switch to “Three sides”.
Result
Area
12cm²
= 0.0012 m²
How it was calculated
S = ½ × a × h = 6 × 4 / 2 = 12 cm²
← Other shapes and the composite shape
02

Formula

and what each letter means

Base and height

Area
S = ½ × a × h

Three sides (Heron)

Semi-perimeter
p = (a + b + c) / 2
Area
S = √(p(p − a)(p − b)(p − c))
Perimeter
P = a + b + c

Right triangle

Hypotenuse
c = √(a² + b²)
Area
S = ½ × a × b
Perimeter
P = a + b + c
Notation
a
base (the side the height is drawn to)
h
height — the perpendicular from the vertex to the base
p
semi-perimeter in Heron’s formula
03

Worked example

base and height
Givena = 6 cm, h = 4 cm
Solution
S = ½ × a × h = 6 × 4 / 2 = 12 cm²
Answer: area — 12 cm².
04

Common mistakes

The formula ½ a·h takes the height, not a slanted side. If you only know the sides, use Heron’s formula.

Don’t forget the half: a × h is the area of a rectangle, the triangle is half of it.

Sides 3, 4 and 10 do not make a triangle: each side must be shorter than the other two combined.

05

Nearby shapes

TrapezoidS = (a + b) / 2 × hParallelogramS = a × hPyramidV = ⅓ a²hCalculatorAll 19 shapes, the composite shape and hectares →
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Length converter

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%

Percent and VAT

Shares, mark-ups, VAT
2·8·16

Number bases

Binary, octal, hex

Updated

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