SAT Practice Questions: 30-60-90 Triangles - dummies

SAT Practice Questions: 30-60-90 Triangles

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?
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?

1. The correct answer is Choice (A).
You can find the area of an equilateral triangle by using the formula

where s is any of the sides, including the base:

You can also consider the equilateral triangle to be two 30-60-90 triangles, giving the triangle a height of

then use the
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

The 2 is the hypotenuse, making the other two sides 1 and

These numbers are also the base and height, so plug them into the formula for the area of a triangle: