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Lesson 2: Areas of 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 $A=\frac{1}{2}bh$‍

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 $bh=4×5=20$ square units, so the area of the triangle is $\frac{1}{2}bh=\frac{1}{2}×4×5=10$ 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?
units${}^{2}$

Practice problem 2: right triangle

What is the area of the triangle?
units${}^{2}$

Practice problem 3: one vertex is hanging over the side

What is the area of the triangle?
units${}^{2}$

Want to join the conversation?

• Do we need math in our life mostly people dont use it in the modern world only high tec jobs do
• math is the foundation of everything. think about it you need to know how many dollar socks you can get, the amount of tip to leave, or even what your Christmas gifts will cost.
• This is very helpful! Does this work for all triangles?
• Yes! it works for all triangles!
• why do you want to find area of a triangle
• If you want to know the height of anything like a building or a tree or a telephone pole, you can use geometry, or triangulation to figure it out. Knowing A=1/2bXh is very important for all kinds of measurements in the real world.
• Lol, I'm 17 going to 12th grade next summer. Just reviewing the fundamentals of math. Hey kids make sure you guys focus and not taking anything for granted. It will help you once you get to higher level math, and keep you ahead of the comp. Keep Khanning!
• Literally in the same situation. I went through geometry and algebra 1 but got by without studying and don't remember a thing, now Im going into 12th grade in 2 weeks. Khan Academy is saving my soul rn
• i feel like monkeys can solve this but not me XD jk
• Don't worry, the area of a triangle is base x height then after that divide it by two. if the number is and odd number, add a decimal to it like for example 11 your total for base times height you divide it by two and you get 5.5 as your answer. Hope this helps
(1 vote)
• 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
• is there any other formula which can be used to find an area of a triangle