Find perimeter of flag... 
I took a practice SAT test, and I didn't do as well on the math portion as I was hoping to. I ran into a problem like this (not geometry, but one that took me too much time) in each section and didn't have time to check my work..
Anyway, the problem shows a flag like this (not drawn to proportion) and gives the following information: the flag is made of two identical, intersecting equilateral triangles. All three line segments on the right hand side are 10 inches long. 
It asks for the perimeter of the flag...
I didn't figure out how to solve the problem until after I had taken the test and thought about it. It took me too long to realize that the length of the sides of the larger triangles was 20 inches. I still don't have a mathematical basis for knowing that, it just logically made sense. 
What conclusions should I have made upon seeing the flag and reading the information? What would have been the best way to solve this?
 A: You are right that the side of the triangles is 20 inches, as it is made up of two 10 inch segments.  The triangles are equilateral, so all the sides are 20 inches.  Because all the angles are 60 degrees, the small triangle is equilateral, too, and has a side of 10 inches.  The total perimeter is then two 20 inch long sides, the two 10 inch short sides on the left, and the given 30 inch segment on the right, for a total of 90 inches.
A: Here's the first tip I give to any student about the SAT math portion:

Stop reading the question when you get to the first comma. 

Many SAT math problems are in the form 
"If ... (statement about the picture, $x,y,z$, etc) ....., then what is.....? 
And the question (which is after the comma) usually requires more than one step to complete. 
Example: "If $(x + y)^2 = 121 \ \ $ and  $xy = -13$, then what is the value of $x^2 + y^2$ ?"
This problem can be tricky if we focus on the question (i.e. on directly determining the value of $x^2 + y^2$). Instead, let's stop when we get to the comma. 
So we have $(x + y)^2 = 121$ and ... well, let's work with that!
$(x + y)^2 = x^2 + y^2 + 2xy$, by FOIL-ing/distributive property/etc, and this equals $121$. So $$(x+y)^2 = x^2 + y^2 + 2xy = 121$$
Since $xy = -13$, we can substitute this in, to get: $$x^2 + y^2 + 2(-13) = 121$$ From this you should be able to see the answer. 

Like I said, many SAT math problems are like this: They give data in the "if" part of the question, sufficient to draw some conclusion(s), and then ask for a conclusion that may be 2-3 steps beyond what you can immediately see. 
The easiest way to overcome this is to Stop reading at the comma!
