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Middle school📐Geometry●○○○○· 4 min
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Triangle area: half of the surrounding rectangle

Base × height ÷ 2: the formula comes from a rectangle cut in half. The visual proof that makes the formula obvious.

The formula

Area(△)=base×height2\text{Area}(\triangle) = \dfrac{\text{base} \times \text{height}}{2}

Where the « ÷ 2 » comes from

The triangle is half a rectangle

Étape 1 / ?

baseheight
A right triangle: base = 12, height = 8.
complete rectangle
We complete it with an identical triangle: that makes a rectangle.
Area = (12 × 8) / 2 = 48
Rectangle area = base × height. Triangle area = half of it.

It works even for a non-right triangle

The « height » of a non-right triangle is the perpendicular segment from the base to the opposite vertex. The surrounding rectangle still exists — the formula still holds.

The classic mistake

Don’t confuse height and side. Height is the perpendicular distance, not the length of the slanted side.

?Your turn

A triangle has a base of 10 cm and a height of 6 cm. What's its area?

#area#triangle#rectangle#proof

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