Last week, The College Board announced massive changes to the SAT. Gone are the historically arcane “SAT words” and the required essay section. And making its triumphant return is a score out of 1600 — not 2400 like it’s been since 2005. While this news may make students nervous (“Is the studying I’m doing right now going to be a waste?”) the truth is that this new version of the SAT isn’t being offered until Spring 2016. So those studying right now for Spring or Fall 2014 tests should stay the course on the study plan they already have in place.
To help us through a tricky geometry problem — one you’d find on the current version of the exam —is Atasha J., a Harvard graduate who gets great reviews for her SAT prep, biology and algebra lessons. Here’s the confusing question:
This SAT questions is a bit tricky because it combines several geometric principles into one question. If you forget one of those principles, it will be very difficult for you to answer this question. I recommend that students review the basics of geometry as much as they can, because the geometry questions aren’t hard per se, they just requires students to be able to think in a puzzle-like manner.
The first thing to recognize with a problem like this is the fact that the height of the triangle is equivalent to the diameter of the circle. Because we are given the area of the circle, we can then find the circle’s diameter, which also gives us the height of the triangle.
Now that we have the height of the triangle, the final step is for us to find the base of the triangle. There are few different methods to approach finding the base, but they all start with recognizing that triangles ADB and ADC are 30-60-90 triangles. One helpful ratio to remember is that for 30-60-90 triangles, the sides of the triangles will be x:x:2x, respectively. Because we have the measure of one side of the triangle and the measure of the angles, we could use trig functions to find the value of line segment DB which is half of the base. However, if will save you a lot of time on the day of the exam if you use the ratios mentioned above.
Once we find the measure of the base, we can then plug that value and the value of the height of the triangle in the triangle area formula to find the overall area of triangleABC. And we find that the final answer is (C).
This problem is definitely on the tricky side, and requires you to think through your approach before you start. If it’s been a few years since you tackled geometry, our online geometry tutors can help you get refreshed on the most important formulas and principles. For general SAT math help, set up a lesson with Atasha, or choose one of our other online SAT Math tutors.