# Tag Info

### How to justify formula for area of triangle (or parallelogram)

An alternative explanation, one formula to rule them all, so to speak: There is a single formula that comprises the areas of a rectangle, parallelogram, trapezoid and triangle: $\qquad$The area equals ...
• 5,760

### How to justify formula for area of triangle (or parallelogram)

As requested, a version without the encompassing rectangle. (Or at least one that has less algebra.) The initial triangle with base $b$ and height $h$: Double it, to get a parallelogram with twice ...
• 5,873

### How to justify formula for area of triangle (or parallelogram)

I do recommend going through the rectangles and parallelograms, but I just want to note that your intuition about starting with a right triangle and moving the top around is Cavalieri's principle and ...
• 7,348

### How to justify formula for area of triangle (or parallelogram)

If you do want to deal with a triangle whose known base has an obtuse angle at one end (so that the height is not located between the endpoints of this base), you can use subtraction. I want the area ...
• 21k
Accepted

### How to justify formula for area of triangle (or parallelogram)

Remember that this is an explanation, not a proof. You don't need to define precisely how to construct the encompassing rectangle. Just demonstrate drawing an encompassing rectangle and have the 8-...
• 11.5k
In the comments, it seems some people are surprised that $4 \times 8$ and $6 \times 8$ have such low accuracy (as shown in the table in the accepted answer). There's actually a cognitive principle ...