In a lateral projection, the area can be represented by the expression

• A. measured area on map / scale factor square
• B. true area × scale factor square
• C. measured area on map × scale factor square
• D. true area / scale factor

Answer: (D)

Area distortion and scale factors in map projections determine how true areas shrink or grow on the map. For a lateral projection, the area represented on the map is tied to the true area by the area’s scale factor, but in this convention the map area is the true area divided by that factor. In other words, if the local area scale factor is s, the area you’d see on the projection equals true_area divided by s. This is why the expression uses true area divided by the scale factor.

The other forms would imply applying the scale factor in the wrong way (such as multiplying by it or using its square), which doesn’t match how area distortion is represented under this projection’s convention.