If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Triangle missing side example

Dive into the world of triangles! Learn how to find a missing piece using just the area and height. Apply this knowledge to solve puzzles and explore the magic hidden in these three-sided shapes. Join the triangle adventure!

Want to join the conversation?

  • purple pi purple style avatar for user Minh Tran
    So, the 11 is useless? For this problem?
    (67 votes)
    Default Khan Academy avatar avatar for user
    • primosaur seed style avatar for user Ian Pulizzotto
      Yes you are correct that the 11 would be useless for this particular problem. An important skill in mathematics is separating useful information from useless information. Sometimes useless information is included on math test problems to test the students' ability to separate useful information from useless information. The useless information is sometimes used to create wrong answer choices (traps) on multiple choice test questions.
      (74 votes)
  • starky tree style avatar for user Wolf LEX
    so confusing cant you just do b times h divided by 2
    (23 votes)
    Default Khan Academy avatar avatar for user
    • duskpin ultimate style avatar for user tiannaduffin
      Yes u can, but only if you know the base and height. This skill is about figuring out the missing base/height when you are given the base/height and the area of the triangle

      As an example, let's say the base was 10 and the area was 300. We need to find the missing height. The formula to figuring out the area of a triangle is
      (b * h) / 2. Therefore, (10 * h) / 2 = 300, and
      (10 * h) = 600. 600 / 10 is 60, so h is 60, as
      (10 * 60) / 2 = 300 and (10 * 60) = 600
      (20 votes)
  • aqualine ultimate style avatar for user Moon
    I don't understand why math is so hard
    (24 votes)
    Default Khan Academy avatar avatar for user
  • starky sapling style avatar for user brandon.edwards
    So I paused the video and tried to do it myself, I got the answer right, but I did it differently. I just wanted to make sure it would always work in a situation like this. So I divided 75 by 10 and got 7.5, knowing that this is actually 1/2 the base, multiplied this by 2 and got 15, sounds like a lot, but only took me about 1 minute to do compared to your way, which is why I wanted to know if it was a correct way of doing it.
    (17 votes)
    Default Khan Academy avatar avatar for user
  • boggle yellow style avatar for user Damien
    Why is 11 there if we don't need it? They're scamming us, that's illegal in my book.
    (9 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Austin
    So to find the missing side its just the area divided by half of the hight
    (7 votes)
    Default Khan Academy avatar avatar for user
  • mr pants purple style avatar for user Mrs.Marvel!!!🦸
    Why did they just put the 11 there to distract you?
    (5 votes)
    Default Khan Academy avatar avatar for user
  • piceratops ultimate style avatar for user Axelotl_Hotshot
    I have a question for everybody:
    "How did you guys get through all this hard strategy of math and even get the hang of it? It's weird."
    Everybody says that it is hard but how come you guys know the answer on this whatever area of triangles and the missing side. It is very confusing to me even with the video.
    Can you guys please help me because, and yes, I do know that you have to go through other "EASIER" strategies of math in order to understand harder ones but please comment and tell me the answer to this question.
    (9 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Madison Newman
    How do I work out the area of a triangle if I’m given only one short side length
    (9 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user angriv3250
    I forgot to log in and lost all my progress
    (8 votes)
    Default Khan Academy avatar avatar for user

Video transcript

- [Instructor] The triangle shown below has an area of 75 square units. Find the missing side. So pause the video and see if you can find the length of this missing side. Alright, now let's work through this together. They give us the area, they give us this side, right over here, this 11, they give us this length 10, which if we rotate this triangle, you could view it as an altitude. And in fact, let me do that. Let me rotate this triangle because then I think it might jump out at you how we can tackle this. So let me copy and let me paste it. So if I move it here, but I'm gonna rotate it. So if I rotate the, oh, that is our rotated triangle and now it might be a little bit clearer what we're talking about. This length x that we want to figure out. This is our base and they give us our height and they give us our area. And we know how base, height and area relate for a triangle. We know that area is equal to 1/2 times the base times the height. And they tell us, they tell us that our area is 75 unit squared. So this is 75 is equal to 1/2. What is our base? Our base is the variable x. So let's just write that down. 1/2 times x. And then what is our height? Well, our height is actually the 10. If x is the length of our base, then the height of our triangle is gonna be 10. We actually don't even need to use this 11. They're putting that there just to distract you. So this is going to be our height, times 10. So 75 is equal to 1/2 times x times 10. Or lemme just rewrite it this way. We could say 75 is equal to 1/2 times 10 is equal to 5 times x, is equal to 5 times, lemme do the x in that same color is equal to 5 times x. So what is x going to be? There's a couple of ways you could think about it. You could say 5 times what is equal to 75 and you might be able to figure that out. You might say, okay, let's see, 5 times 10 is 50. And then let's see, I need another 25. So I'd put another 5 there. So it's really 5 times 15. Or you could do it a little bit more systematically. You can divide both sides by what you're multiplying by x. So if you divide this side by 5, 5 times x divided by 5, well you're just going to have an x leftover. But you can't, these two things were equal. So you can't just do it to one side, you have to do it to both sides. So you have to divide both sides by 5. And what's 75 divided by 5? Well that is 15. So you get x is equal to, x is equal to 15. And you can verify that, if x is equal to 15, base times height, times 1/2, well it's 15 times 10 times 1/2 or 15 times 5, which is going to be 75 square units.