Orthogonal Projection

The foot of the perpendicular from a point to a plane is called the orthogonal projection of point onto the plane .
Similarly, the figure , which is formed by the orthogonal projections of all points of a figure onto the plane , is called the orthogonal projection of the figure onto the plane .

If a line is orthogonally projected onto a plane , the result is either a point (if is perpendicular to the plane) or a line (if is not perpendicular to the plane). Therefore, the projection of a polygon onto a plane is either a line segment or another polygon.

In general, the orthogonal projection of a point onto a plane is a point, the projection of a line is either a line or a point, the projection of a polygon is either a polygon or a line segment, and the projection of a sphere is a circle.

Length of the Orthogonal Projection

Let the orthogonal projection of a line segment onto a plane be denoted by the line segment . If the angle between the line and the plane is (where ) and the intersection of the lines and is at point , then: Thus:

Area of the Orthogonal Projection

If a figure lies in a plane and its area is , the area of the orthogonal projection of this figure onto another plane is denoted by . If the angle between the two planes and is (where ), then: