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

Lesson 5: Lesson 9: Formula for area of a triangle# Finding area of triangles

The area of a triangle is found by multiplying one half of the base by the height. In our example, the base is 18 and the height is 6. So, half of 18 is 9, and 9 times 6 equals 54 square units.

## Want to join the conversation?

- In a case when the height isn't given, how do you find out the height?(40 votes)
- In that case, you would use the Pythagorean theorem. That's a squared plus b squared equals c squared. In this specific scenario, the hypotenuse is already given and you would need to know one of the sides or legs in the equation. That means you would square the hypotenuse (the side not connected to a right angle), subtract the square of the side/leg you already know, then take the square root of that final number. That would be the height of the triangle(54 votes)

- Can I also write the solution like this:b*h/2?(20 votes)
- Yes you can because it is the same thing as 1/2*b*h because of the communative property(7 votes)

- what if your base or height is a fraction? PLS HELP ME!(7 votes)
- If the base or height is a fraction, then do the formula as normal. If one is a fraction, and the other isn't, make the whole number a fraction, for example, 3= 3/1. Hope this helps!(8 votes)

- if you multiply width and height then how come i cant divide to find the answer(7 votes)
- You could divide. Instead of doing
**base x height x 1/2**, you could do**base x height/2**.(6 votes)

- OK, is it just base times height and then divide by two? i am kinda confused. can some one plz help me?(6 votes)
- Yes, it is! Whenever finding the area of a triangle, you always want to multiply the base by the height then divide that all by 2. (bh)/2(5 votes)

- This is perhaps a silly question, if so sorry. (Or perhaps covered later?)

Since the length of a triangle’s sides is correlated to the triangle’s angles, shouldn’t it follow that you could calculate the area of a triangle with only the measure of it’s angles?(7 votes) - this doesnt help at all(7 votes)
- I don't understand this, because my teacher told me to do base times height or length times width and then divided by 2 but, he/she said 1/2 x base/width x height/length. Are they both same(4 votes)
- you only divided 2 when you are doing 1/2 b x h(4 votes)

- why do we have to half the base and not the height?? Please Help!!(4 votes)
- The reason why is because then you will get a different product, which will result in a different area.(4 votes)

- How do I find the perimeter of a triangle?(6 votes)
- Add up the sides(0 votes)

## Video transcript

- [Instructor] What is
the area of the triangle? And they're talking
about this triangle here. And like always, pause this video and see if you can figure
it out on your own. All right, now let's
work through it together. So we know that the area of a triangle is going to be equal to 1/2 times our base times our height. Let me do the height in a different color. Times, times our height. So, what is the length of
our base in this scenario? Well, the base is this 18 right over here. Let me highlight it. This length right over here is our base. So the base is 18. And what is the height? Well, the height, we see, is six. They give it to us. They don't always give it to you, but in this example they do. So the height is, the height... The height is, I'm having
trouble with my pen, is six. So now we just have to compute what 1/2 times 18 times six is. Well, let's think about this a little bit. Well, 1/2 times 18 is nine. Nine times six is equal to what? Nine times six is equal to 54. And we are done. This is 54 square units.