Blog

SAT Math: Geometry

Quadrilaterals

If the diagonal of a square has a length of 10, what is the area of the square? 

A)  36

B)  40

C)  50

D)  81

E)  100

 

Knowsys Method

Read the question carefully.   Envision a square that is labeled with the correct diagonal.

Identify the bottom line.  A = ?

Assess your options.  You could try to find the legs of the two triangles created by the diagonal, but that will take time.  You could try to estimate the length of each side, but what if two answer choices are close?  Instead, make sure that you have memorized the formula to find the diagonal of a square.  From that formula you can find the length of each side and the area of the square.

 Attack the problem. 

The formula to find the diagonal of any square is side times the square root of two.  Plug in the diagonal that you have and solve for the side.

 

diagonal square.JPG

This is as far as you need to simplify the side because you are about to square this answer to find the area.  Once you square this fraction, both the fraction and the square root will disappear. 

squarearea.JPG

Loop back.  You solved for your bottom line, so you are finished!  Select your answer.
 

The correct answer is (C). 

This is a medium level question. 

 

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email