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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=12bh

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 12bh=12×4×5=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?
Drag the dot to help you remember the formula.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
units2

Practice problem 2: right triangle

What is the area of the triangle?
Drag the dot to help you remember the formula.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
units2

Practice problem 3: one vertex is hanging over the side

What is the area of the triangle?
Drag the dot to help you remember the formula.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
units2

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