While there's no way to know exactly how many Geometry questions you'll see on test day, an estimated 15% of Quant questions are Geometry-focused — that's a significant amount! Of all of the subjects on GRE Quant, Geometry can be the most work for the least reward. Like all other GRE Quant questions, Geometry questions aren't really testing Math — they're using math to test more important concepts, such as critical thinking, working with limited information, testing assumptions, etc. However, you won't 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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Lumping rules together
That said, there are ways you can 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 memorization. Let’s go through five of the most helpful "sets" of rules here:
First, 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. Now for shapes with two different bases, like trapezoids, you need to find the average of the bases, then multiply by height, but the same general rule holds true.
Second, 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 the 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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A quick aside: for the most part, the distinction between length, width, height, base, etc. doesn't matter at all. You can call whichever side whatever you want, so long as you apply the formulas correctly.
For the rest of the rules, check out the video.
