What is the area, in square centimeters, of a right triangle with a base of centimeters and a height of centimeters?
For right-triangle area questions, immediately recall that the legs (the sides that meet at the right angle) serve as the base and height in the triangle area formula . Multiply the given base and height, then apply the factor, and quickly compare your result to the answer choices, watching out for trap answers that come from omitting the one-half.
Hints
Identify the relevant formula
Think about the formula that uses base and height to find the area of a triangle. It has a fraction in it.
Use the fact that it is a right triangle
In a right triangle, the two perpendicular sides can be used directly as the base and the height in the area formula.
Substitute, then calculate
Once you have the formula, plug in base and height , multiply them, and then apply the fraction from the formula.
Desmos Guide
Compute the area expression
In Desmos, type the expression 1/2 * 6 * 5 (this represents ). The numerical value that appears is the area of the triangle in square centimeters.
Step-by-step Explanation
Recall the area formula for a triangle
For any triangle, the area formula using base and height is:
In a right triangle, the two legs (the sides that form the right angle) can be used as the base and the height because they are perpendicular.
Substitute the given base and height
The problem gives a base of cm and a height of cm. Substitute these into the formula:
First multiply the base and height:
Apply the one-half factor and match the answer choice
Now take one-half of :
So the area of the triangle is square centimeters, which corresponds to answer choice B) 15.