Is Colorado a trapezoid

Answer 1

The shape of Colorado's borders does not form a trapezoid, even on a two dimensional map. On some maps Colorado (and Wyoming) appear to be rectangles...but this is a misleading feature of Mercator projection maps which treat longitudes as parallel when in reality longitude lines converge (get closer) as you move towards the poles. Because of this Colorado's northern border is about 21 miles shorter than its southern border. This might lead one to think that the shape of Colorado is trapezoidal. However, when you use an Equal Area projection type map that shows the northern border to be shorter than the southern border something else happens. The northern and southern borders become curves...actually arcs or sections of circles with diameters of about 6000 miles. Therefore, since a trapezoid would require two parallel lines, the shape of Colorado would not qualify because the northern and southern borders are not lines at all, but portions of circles.

Colorado's shape is close to being a latitude-longitude quadrangle. I say "close" because an LLQ is a portion of a spherical surface and the earth is not exactly spherical...is is an ellipsoid which is wider at the equator compared to other latitudes than a true sphere. The other reason I say "close" is because the shape of Colorado, which was originally defined by Congress based solely on latitude and longitude, has now been defined by the monuments that surveyors put in the ground to define its borders. So...even lines that should have been exactly straight or followed the latitudinal curves of the earth are not because of human error. In some cases these errors are quite significant...up to a mile from where they "should" be.