The triangle ABC has a perimeter measuring 42 cm.
AD = 12
AC = 15
AB = 13
Calculate the area of the triangle.
We have hundreds of course questions with personalized recommendations + Account 100% premium
The triangle ABC has a perimeter measuring 42 cm.
AD = 12
AC = 15
AB = 13
Calculate the area of the triangle.
Given that the perimeter of triangle ABC is 42.
We will use this data to find side CB:
Now we can calculate the area of triangle ABC:
84 cm²
Find the perimeter of the triangle ABC
The base is the side that the height is perpendicular to. In this problem, height AD = 12 is perpendicular to side BC, so BC is your base!
Triangle area requires a base and its corresponding height (perpendicular distance). You can't randomly pick two sides - the height must form a 90° angle with the base.
You must find all three sides using the perimeter! Without knowing BC = 14, you can't calculate the area since BC is the base that corresponds to height AD = 12.
Check your work by ensuring: 1) All three sides add up to the given perimeter, 2) You used the correct base-height pair, and 3) Your arithmetic is accurate.
Yes, but you'd need the height to a different base! This problem gives you height AD = 12 to base BC, so that's the most direct approach.
Get unlimited access to all 18 Triangle questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime