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## 6th grade

### Course: 6th grade > Unit 8

Lesson 2: Areas of triangles# Area of triangles

CCSS.Math:

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

### 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(150 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.(92 votes)

- This is very helpful! Does this work for all triangles?(102 votes)
*Yes! it works for all triangles!*(25 votes)

- why do you want to find area of a triangle(33 votes)
- why...... why have a triangular room.....WHYYYYY(10 votes)

- do you have to divide it by two(19 votes)
- if you dont you are technically doing normal rectangle area(12 votes)

- the triangles are hard to do sometimes.(16 votes)
- yea but youjust have to do it a ot(2 votes)

- i feel like monkeys can solve this but not me XD jk(18 votes)
- is there any other formula which can be used to find an area of a triangle(14 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|(5 votes)

- I will accept all the help I can get because I can really make use of it.(10 votes)
- 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.(8 votes)

- I dont understand what to do after you mutiply(5 votes)
- After you multiply the base and height of the triangle, you have a parallelogram that is twice the size of the triangle you started out with. To get the area of your triangle and not this parallelogram, you have to divide by 2.

You might be interested in this Khan Academy video, which tells you why the formula for a triangle is the way it is - https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/geometry-area-triangle/v/triangle-area-proofs(11 votes)

- Is math really “that important?” That’s why god invented calculators isn’t it.(7 votes)
- yes cause without math millions of things wouldn't be invented just like khan academy. computers, phones, tablets, buildings, and even parks wouldnt be here if it weren't for math, that's why its so important even just for life(5 votes)