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:
