Perceptual Ability Study Guide for the DAT

Spatial Relations/3-D Form Development

In this section, you are given a flat, two-dimensional representation of a three-dimensional object, and you must imply what the formed three-dimensional object will be. This two-dimensional pattern is known as a net, which, when folded along specific lines, can be used to create a three-dimensional shape. A net is effectively what you would get if you flattened out a three-dimensional shape.

The following shapes are nets, since their sides can be folded into a three-dimensional shape, specifically the three-dimensional shapes below them.

Some nets may also have shading. The shading will carry over from the two-dimensional to the three-dimensional shape and must also be considered. Here are two examples:

The nets above form the following figures when folded:

The General Procedure

For some, this part of the exam has the potential to be the hardest portion. However, it can be relatively easy depending on how you approach the questions. Instead of looking at the flat net and trying to make the mental image in your head, look instead at the answer choices and see if there are any choices that you can eliminate. There are a few ways to do this, and one includes the faces on shapes in the answers. If a shape has no line crossing a face, then that side is one singular piece. This means that the net of the three-dimensional shape must have that shape within it. If that shape is not within the net, then you can eliminate the answer. Consider the shapes below:

The horizontal lines across the face of rectangle 1 tell us that we must fold along those lines, so we must look for four smaller rectangles in the net. Since no lines besides the borders are present in rectangle 2, the entire shape of rectangle 2 must be present in the net (because it is not divided in any way).

You must also identify unique shapes in the two-dimensional net. There will always only be one correct choice, and because of that, the two-dimensional and three-dimensional shapes must carry the same unique characteristics/shapes. Any answer choices that do not contain key, unique faces like that in the two-dimensional object must be eliminated.

A similar method is used for shaded objects. There will often be a unique face caused by the type of shading on the two-dimensional shape. Just like with the uniquely shaped faces, you must eliminate all choices that do not contain all of the uniquely shaded faces.

Examples

The following examples should solidify this type of question format for you.

Example 1

The correct answer is A. When considering the given net, there is one unique shape that should stand out, highlighted here in red:

Since this shape has no lines crossing through it, it must be a complete face and will be represented in the final three-dimensional figure. Knowing this, when we look at option A, it does have this characteristic, so let’s move on to the other options and see if they also match this face. Both B and C have similar face shapes to that of the given net, but they do not match exactly, so we can eliminate them both. Choice D is clearly not a match, as nothing close to the net’s face is represented. Therefore, we can eliminate all choices except A, and we have an answer without having to consider any mental manipulations of the net.

Example 2

The first step here is to identify key aspects of the shadings and how they are related to one another. One notable thing is that one of the shadings is directly underneath a curved face. The shadings are also not touching (and will not touch when folded). Using this information, we can start eliminating answers. Choice C only has one shaded in portion, so it can be eliminated. The shade faces on choice B are touching, which also conflicts with our observations, so it is eliminated. Choice D does have the shading directly underneath a curved face, but the shaded portion is significantly longer than what we are given. This means that either two shadings are touching each other, or the shading on D is simply larger than what we want. In either case, D is eliminated, and A is the only valid answer.