What is the plane projective theorem?

Area projection theorem: "The projection area of a plane figure is equal to the area s of the projected figure multiplied by the cosine of the included angle between the plane where the figure is located and the projection plane."

COSθ=S projective /S primitive

(The area of a planar polygon and its projection are S primitive and S projection respectively, and the sharp dihedral angle formed by its plane is θ)

Proof idea: Because the projection is to scale the length of the original figure (the height in the triangle) and the width is unchanged, and because the area ratio of the plane polygon = the square ratio of the side length. So it is the ratio of the length of the figure (called the height in the triangle). Then this ratio should be the cosine of the angle formed by the plane. Make a right-angled triangle on two planes so that the hypotenuse and right-angled edge are perpendicular to the edge (that is, the intersection of the plane where the original polygon is located and the projection plane), then the hypotenuse and the other right-angled edge of the triangle are the length ratio of its polygon, that is, the area ratio of the plane polygon, and substitute this ratio into the plane triangle for operation.