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### Course: 7th grade foundations (Eureka Math/EngageNY) > Unit 1

Lesson 4: Topic D: Foundations# 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 $A={\displaystyle \frac{1}{2}}bh$

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

### Practice problem 2: right triangle

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

## 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(189 votes)
- 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.(143 votes)

- This is very helpful! Does this work for all triangles?(122 votes)
*Yes! it works for all triangles!*(48 votes)

- why do you want to find area of a triangle(51 votes)
- why...... why have a triangular room.....WHYYYYY(28 votes)

- 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!(48 votes)
- 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(21 votes)

- do you have to divide it by two(21 votes)
- if you dont you are technically doing normal rectangle area(17 votes)

- the triangles are hard to do sometimes.(23 votes)
- yea but youjust have to do it a ot(4 votes)

- i feel like monkeys can solve this but not me XD jk(26 votes)
- is there any other formula which can be used to find an area of a triangle(19 votes)
- 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|(10 votes)

- I don't really see how the putting the shape together can help me solve the problems on some of them. Other problems it works great.(22 votes)
- Bro, I was in 4th grade last year (going to 5th this year and I am already in 6th grade math) and I am so ahead of my class but this video was helpful. You just have to pay attention to it and it will be super easy. I am a fast learner depending in what I am doing, it can be fun!! Just take my advice!(16 votes)
- ya that what im doing. jump two grades ahead and your good you dont half to worry bout anything, my bro is skiping geometry at 7th grade(geomatry is 10 grade)he's going to do pre-calc next year

let's hope he past's the skiping class!(4 votes)