Area of Triangle in Terms of Side and Altitude/Dissection Proof

Theorem

The area of a triangle $\triangle ABC$ is given by:

$\dfrac {c \cdot h_c} 2 = \dfrac {b \cdot h_b} 2 = \dfrac {a \cdot h_a} 2$

where:

$a, b, c$ are the sides

$h_a, h_b, h_c$ are the altitudes from $A$, $B$ and $C$ respectively.

Dissection Proof

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dissection proof