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SAT Math: Geometry

SAT Question of the Day

The SAT question of the day is a Geometry question.  Geometry questions can be a lot of fun if you look at them like logic puzzles.

Read the question carefully:  Notice that there is a diagram of a figure with many different sides that are labeled.  The problem tells you that all the angles in the polygon are right angles.  That means that you will be dealing with squares and rectangles.  

Identify the bottom line:  What is the area of the polygon?  Note this as "A = ?"

Assess your options:  You could try to start drawing lines within the polygon to create rectangles and squares.  Then you could add up the areas of each of these shapes.  That will take you a long time.  Instead, look at the shape as a whole.  It looks like a rectangle with a little bit taken out of it.  Subtracting that little bit from the area of the whole will be a much faster method to solve this problem. 

Attack the problem

The big rectangle has a length of 12 and a width of 9.  To find the area, you multiply length times width.  You have

9 × 12

Now look at the portion that is missing from this rectangle.  It looks like there are two smaller rectangles that have been cut out.  The first is a rectangle that is 3 × 2.  You now have:

9 × 12 - 3 × 2

That leaves you with the corner piece that has been removed.  It looks like a square.  Only one side is labeled with a 2, so you must confirm that the other side also has a length of 2.  Look at the horizontal lines labeled 3 and 7.  3 and 7 would add to 10, but you know that the larger shape only has a width of 9.  That means that these two lines overlap for a length of 1.  Since the part you are looking at is under the 3, and you know that 3 - 1 = 2, you have confirmed that the bottom corner is a square with the dimensions 2 × 2.  You have now accounted for all of the space that was taken away from the large rectangle.  

 9 × 12 - 3 × 2 - × 2

108 - 6 - 4

98

Loop Back:  Does the number 98 represent the area of the entire polygon?  Yes. 

The correct answer is (D). 

 On sat.collegeboard.org, 49% of the responses were correct. 

ACT Question of the Day

The ACT question of the day is a Science question that has already been addressed on this blog: click here to see an explanation.

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