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### Course: 6th grade (Illustrative Mathematics) > Unit 1

Lesson 5: Lesson 9: Formula for area of a triangle# 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?

- So, the 11 is useless? For this problem?(67 votes)
- 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.(71 votes)

- so confusing cant you just do b times h divided by 2(23 votes)
- 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)

- I don't understand why math is so hard(24 votes)
- The more you understand math, the more you will like it. Trust me, in the beggining, I hated math, because I didn't understand it and thought it was too hard. But now, I understand it better, and I enjoy doing math now.(14 votes)

- 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.(16 votes)
- I agree, this method is quite efficient. I recommend doing this if your stuck on doing the equations.(9 votes)

- Why is 11 there if we don't need it? They're scamming us, that's illegal in my book.(9 votes)
- They put it there as mostly a set up to see if you listened or not I'm guessing(3 votes)

- So to find the missing side its just the area divided by half of the hight(7 votes)
- Why did they just put the 11 there to distract you?(5 votes)
- Questions/Teachers love to confuse you, the distractions make you confused and get the question wrong. Hope you got the answer correctly!(10 votes)

- 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) - How do I work out the area of a triangle if I’m given only one short side length(9 votes)
- I forgot to log in and lost all my progress(8 votes)

## 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.