# 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

**What is the area of an equilateral triangle with a base of 4?**

- A certain right triangle has a hypotenuse of 2. If one of the angles is 30 degrees, what is the area of the triangle?

## Answers and explanations

**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

**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: