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## Algebra basics

### Course: Algebra basics>Unit 1

Lesson 9: Area 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 $A=\dfrac{1}{2}bh$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?

• 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
• why...... why have a triangular room.....WHYYYYY
• 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
• i feel like monkeys can solve this but not me XD jk
• is there any other formula which can be used to find an area of a triangle
• 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|