Here’s an important thing to remember: all figures on the SAT are drawn to scale unless indicated otherwise. In other words, if it doesn’t say “Note: figure not drawn to scale,” underneath it, it is drawn to scale. Most figures on the SAT are drawn to scale, which means it’s a good idea to guesstimate whenever possible.
Guesstimating could mean actively trying to eyeball relative angle measures, areas, or segment lengths, or it could mean sliding pieces of the diagram around in your mind. You might still end up doing some math because guesstimating doesn’t lead you all the way to an answer. But it’s important that you not waste the opportunity when a diagram is drawn to scale. Let’s dig right into an example:
- The figure above depicts two intersecting diameters of two concentric circles of radius 6 and 10. If the diameters are perpendicular, what is the area of the shaded regions?
STOP DOING MATH! You need almost none of it to solve this problem. How can you guesstimate this?
Well, what’s the area of the large circle? 100π. What’s half of that? 50π. Good, the answer is (B). Done.
Why? Glad you asked. What happens if I rearrange the pieces of the puzzle?
Note that guesstimating doesn’t just apply to shaded regions. You can use it to solve all kinds of geometry questions. As long as a figure is drawn to scale, you should ponder the implications of guesstimate for a few seconds before you start doing any math. This takes practice, but I promise you it’s worth it when you become proficient.
The questions below can be solved with math, but your mission is to solve them with guesstimate. Make me proud.