A Erika John from PrepScholar GRE explains, of all the subjects on GRE Quant, geometry can be the most work for the least reward. Like all other GRE Quant questions, geometry questions do not really test your math skills. Rather, they’re using math to test more important concepts, such as critical thinking, working with limited information, and testing assumptions, etc.
However, you will not get a chance to demonstrate your ability in these important skills if you don’t know the math being used to test them. For geometry, that math is memorization-heavy – more so than any other type of Quant question on the test. A single question may utilize a variety of formulas and rules, from triangles to circles to quadrilaterals to lines and angles, and missing even one step in a multi-step problem can prevent you from answering the question.
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That said, there are ways to make the most of these challenging problems, both in your study and in your approach to the problems themselves.
The first thing to know is that while there are many rules and formulas to memorize, many can be lumped together for easier recall. The video goes through five of the most helpful sets of rules.
For example, you can find the area of any quadrilateral by multiplying the length of the base times the length of the height. This is also commonly expressed as length times width. Squares, rectangles, parallelograms, trapezoids – all length times width. When it comes to shapes with two different bases, such as trapezoids, you need to find the average of the bases, then multiply by height, but the same general rule holds true.
Another key tip has to do with the volume formula of three-dimensional solids. If a three-dimensional solid has the same diameter throughout (in other words, it has the same shape on the top as on the bottom), the volume formula will be the area of the base times the height of the solid. So for any solid based on a quadrilateral, like a rectangular prism or a cube, the volume will be the length of the quadrilateral times the width of the quadrilateral, times the height of the prism. For a cylinder, the volume will be pi times the length of the circle’s radius squared, times the height of the cylinder. For a triangular prism, the volume will be one half the length of the triangle’s base times the height of the triangle, times the height of the prism itself. This will not work for shapes with inconsistent diameters such as cones or pyramids.
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For the most part, the distinction between length, width, height and base, etc. does not matter at all. You can call whichever side whatever you want, so long as you apply the formulas correctly.
To get to know the rest of the tips about GRE geometry, go ahead and watch the full video tutorial!