Making Sense of SAT Math

A couple weeks ago, we discussed the SAT Math “Reference Information” box and whether or not the formulas should be memorized ahead of time. We received a lot of good comments, but this one from Sparkler ericbm2 piqued our interest:

To memorize these formulas, just try to understand them. Try to visualize what it is saying. Doesn't it make sense that the area of a triangle is half of the rectangle around it? Also, the area of a circle is the area, which is in square units. Square units. pi x r-squared?

What a great tip! We couldn't agree more. It is important to understand the logic behind these formulas, instead of just memorizing them for the sake of the test. Understanding them not only gives you a better chance at getting the question right, but it will also help you remember the formula.

Let’s take a look at a one of ericbm2's suggestions: The area of a triangle is half of the rectangle around it. This means that if a triangle and rectangle have the same length and width (or base and height), the area of the triangle is half of the area of the rectangle. Let’s make some diagrams to see how this works.

We have a triangle inside of the rectangle: the base of the triangle is equal to the length of the rectangle (b = l) and the height of the triangle is equal to the width of the rectangle (h = w). The triangle’s area is half of the rectangle’s area. This makes total sense, right?You can tell from the diagrams that the triangle’s area is half of the rectangle.

Keep in mind that the triangle could look different and have the same base and height measurements. Take a look:

This triangle has the same base and height (b and h), so it has the same area as the triangle above. The fact that the triangle’s area is half of the rectangle’s area is a little less visually obvious. But look at this:

Divide the rectangle and triangle into left and right halves. Both “1” sections have the same area, and both“2” sections have the same area. Why? Because these sections are triangles: The “1” triangles have the same base and height, as do the “2” triangles.

The triangle in the center has a “1” section and a “2” section. The rectangle has two “1” sections and two “2” sections. Therefore, the rectangle has twice the area of the triangle.

All of the formulas that you need to know for SAT Math can be boiled down in this same way. Try to understand them, visualize how they work, and see how they relate to each other.

Find more help with SAT Math here.

What formulas do you have trouble with? Share your questions and your insights in the comments.

Related Post: The SAT Math Formula Trap