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

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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
unitsstart superscript, 2, end superscript

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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
unitsstart superscript, 2, end superscript

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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
unitsstart superscript, 2, end superscript