SAT: 1,001 Practice Questions For Dummies
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When you encounter a question on the SAT Math exam where you have to find the area of a triangle, you may end up treating it as a 30-60-90 triangle, even if it's equilateral. (Fun fact: an equilateral triangle can be thought of as two 30-60-90 triangles!)

The following practice questions ask you to find the area of an equilateral triangle and then to find the area of a right triangle given only its hypotenuse and one of its angles.

Practice questions

  1. What is the area of an equilateral triangle with a base of 4?
    SAT1001_eq0801
  2. A certain right triangle has a hypotenuse of 2. If one of the angles is 30 degrees, what is the area of the triangle?
    SAT1001_eq0802

Answers and explanations

  1. The correct answer is Choice (A). You can find the area of an equilateral triangle by using the formula
    SAT1001_eq0803
    where s is any of the sides, including the base:
    SAT1001_eq0804
    You can also consider the equilateral triangle to be two 30-60-90 triangles, giving the triangle a height of
    SAT1001_eq0805
    then use the
    SAT1001_eq0806
  2. The correct answer is Choice (A). If one of the angles is 30 degrees, the other angle is 60 degrees, making this a 30-60-90 triangle, with a side ratio of
    SAT1001_eq0807
    The 2 is the hypotenuse, making the other two sides 1 and
    SAT1001_eq0808
    These numbers are also the base and height, so plug them into the formula for the area of a triangle:
    SAT1001_eq0809

About This Article

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About the book author:

Ron Woldoff is the founder of National Test Prep, where he helps students prepare for the SAT, GMAT, and GRE. He is the author of several books, including GRE For Dummies and 1,001 GRE Practice Questions For Dummies.

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