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Area of triangles

Intuition for why the area of a triangle is one half of base times height. 

Intuition for why the area of a triangle is A, equals, start fraction, 1, divided by, 2, end fraction, b, h

To see why the formula makes sense, drag the dot all the way to the right:
Whoa! You made a rectangle that's twice as big as the triangle! The area of the rectangle is b, h, equals, 4, times, 5, equals, 20 square units, so the area of the triangle is start fraction, 1, divided by, 2, end fraction, b, h, equals, start fraction, 1, divided by, 2, end fraction, times, 4, times, 5, equals, 10 square units.
Key intuition: A triangle is half as big as the rectangle that surrounds it, which is why the area of a triangle is one-half base times height.

Practice problem 1

What is the area of the triangle?
Drag the dot to help you remember the formula.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
unitssquared

Practice problem 2: right triangle

What is the area of the triangle?
Drag the dot to help you remember the formula.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
unitssquared

Practice problem 3: one vertex is hanging over the side

What is the area of the triangle?
Drag the dot to help you remember the formula.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
unitssquared

Want to join the conversation?

  • duskpin seed style avatar for user Stephanie Pearce
    Do we need math in our life mostly people dont use it in the modern world only high tec jobs do
    (122 votes)
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  • mr pink green style avatar for user maryannefalli
    This is very helpful! Does this work for all triangles?
    (91 votes)
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  • aqualine seed style avatar for user LilD
    why do you want to find area of a triangle
    (22 votes)
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    • starky ultimate style avatar for user Slushie
      Finding the area of a triangle by itself may often not feel like a very useful skill, but to understand math concepts like calculus and trigonometry, you need to start somewhere, and that place won't be the very top. Like MCFCguy stated:

      "Whether we like math or not, math is influencing our daily lives. Let's imagine a world without math. Our currencies wouldn't function because they would all just be pieces of paper of equal value without numbers on them. Buildings would not stand up straight and would almost certainly cause casualties because we would have no concept of angles. Our roads would not be straight because we don't know anything about geometry or trigonometry. We wouldn't have internet or phones or computers. Which would mean no Khan Academy. We wouldn't have boats, cars, or airplanes. And we certainly wouldn't have spacecrafts. But even if we did, we would never figure out how to launch them effectively every time. So, in short, even if you hate math, if it didn't exist, we would have almost none of the modern conveniences that we have grown accustomed to."

      Isaac Newton (and the other German dude) weren't just sitting under an apple tree when he got hit in the head with an apple (I know he didn't actually get hit in the head with an apple) and suddenly was granted the knowledge of the equation for gravity, or just invented calculus without knowing anything about math. If you wan't to discover new things, invent new things, create new things, it won't be as soon as you get hit in the head with an apple. You will need to understand math, in any job that is legitimately contributing to humanity. I am not saying every job requires you to understand calculus and special relativity, but you do need math.

      In conclusion, Humanity has sent rockets to space, because of complex math. That complex math only exist because of simple things like this.

      We need to be able to find the area of a triangle, so that we can learn trigonometry. So that we can send rocket to space. Colonize Mars. Build Stellar Engines.
      (57 votes)
  • blobby green style avatar for user myaphill1
    do you have to divide it by two
    (12 votes)
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  • male robot donald style avatar for user palwasha.asif
    is there any other formula which can be used to find an area of a triangle
    (12 votes)
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    • aqualine ultimate style avatar for user Elmion
      1) abc/4R (R is radius of circumscribed circle)
      2) r/2×(a+b+c) (r is radius of inscribed circle)
      3) If you know the coordinates of the three points, use the shoelace formula
      1/2×|x₁y₂+x₂y₃+x₃y₁-x₂y₁-x₃y₂-x₁y₃|
      (2 votes)
  • duskpin sapling style avatar for user Shannon Ritchie
    the triangles are hard to do sometimes.
    (8 votes)
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  • blobby green style avatar for user Elijah Blackmon
    I will accept all the help I can get because I can really make use of it.
    (5 votes)
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  • duskpin seedling style avatar for user Taylor :]
    I dont understand what to do after you mutiply
    (4 votes)
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  • duskpin seed style avatar for user ayse.sahingoz
    i feel like monkeys can solve this but not me XD jk
    (6 votes)
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  • starky sapling style avatar for user 2028ethanyork
    why did you make this so annoying and dumb
    (4 votes)
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