Projected area

Projected area is the two dimensional

.

The geometrical definition of a projected area is: "the rectilinear parallel projection of a surface of any shape onto a plane". This translates into the equation:

where A is the original area, and ${\displaystyle \beta }$ is the angle between the normal to the local plane and the line of sight to the surface A. For basic shapes the results are listed in the table below.^[1]

Projected area for basic shapes^[1]

Shape	Area	Projected area
Flat rectangle	${\displaystyle A=L\times W}$	${\displaystyle A_{\text{proj}}=L\times W\cos {\beta }}$
Circular disc	${\displaystyle A=\pi r^{2}}$	${\displaystyle A_{\text{proj}}=\pi r^{2}\cos {\beta }}$
Sphere	${\displaystyle A=4\pi r^{2}}$	${\displaystyle A_{\text{proj}}={\frac {A}{4}}=\pi r^{2}}$

See also

• Surface area

References