A right triangle has a base of and a height of . What is the area of the triangle?
For SAT geometry questions about the area of a right triangle, immediately write the formula and identify the base and height as the two sides forming the right angle. Substitute the given lengths, multiply them, and then take half—double-check you didn’t forget the , since that’s a very common trap on the test.
Hints
Think about the area formula
What is the formula for the area of any triangle in terms of its base and height?
Use the right triangle’s legs
In a right triangle, the base and the height are the two sides that form the right angle. Which numbers in the problem are those sides?
Apply the formula carefully
Multiply the base and height together first, then remember to take one-half of that product.
Desmos Guide
Compute the triangle’s area
In Desmos, type 1/2 * 6 * 3 and look at the numerical result. That value is the area of the triangle in square centimeters.
Step-by-step Explanation
Recall the area formula for a triangle
For any triangle, including a right triangle, the area formula is:
In a right triangle, the base and height are the two sides that meet at the right angle.
Identify and substitute the base and height
From the problem:
- Base
- Height
Substitute these into the area formula:
Calculate the area
First multiply the base and height:
Now take half of 18:
So, the area of the triangle is , which corresponds to choice D.