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.

### Unit 5: Lesson 2

Area of parallelograms and triangles

# 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 $A=\dfrac{1}{2}bh$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?
unitssquared

### Practice problem 2: right triangle

What is the area of the triangle?
unitssquared

### Practice problem 3: one vertex is hanging over the side

What is the area of the triangle?
unitssquared

## Want to join the conversation?

• why do you want to find area of a triangle
• 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.
• This is very helpful! Does this work for all triangles?
• Yes! it works for all triangles!
• do you have to divide it by two
• if you dont you are technically doing normal rectangle area
• the triangles are hard to do sometimes.
• yea but youjust have to do it a ot
(1 vote)
• I will accept all the help I can get because I can really make use of it.
• Use the formula base (usually the bottom part of the triangle) times the height (the distance from the very top point of the triangle down to the middle of the base) divided by 2. Usually the height is represented as a dotted line.
• I dont understand what to do after you mutiply
• why did you make this so annoying and dumb
• mabe u should watch the video its simple really
(1 vote)
• the multiplcation is hard like 20 times 8
• so you are going to multiply the 2 by the 8 and add a 0 to the end of your answer (since it is 20 and not 2) Example:

20 x 8
2 x 8 = 16
which means if you add a 0 to the end it becomes 160
(1 vote)
• How do you guys like figuring out the area of triangles? (: