So I've always had problems remembering the formula for the area of a triangle. Until last night, when my mom pointed out that a triangle is half of a square, and suddenly it all made sense (she also remarked that she had had the same problem with that formula until someone had pointed that fact out to her).
It's not that we're missing the obvious. The reason is that math teachers don't (usually) explain the formula for the area of a triangle in those terms, and most people's brains are not wired to make the connection on their own, especially at the point in their development when they are first introduced to these formulas (in fact, the way math classes are often structured can even aggravate the problem, as the formula for the area of a square is introduced much earlier than the formula for the area of a triangle).

L x W = Area, where L is the length of the square and W is the width of the square

1/2 x B x H = Area, where B is the base of the triangle and H is the height of the triangle

For those of you who are more visually inclined:

this is exactly how my teachers in elementary school taught the formula. you can also point out that the sum of a triangle's angles are 180 and a square is 360 (360/180 = 2). a pentagon's angles sum to 540. it can also be divided into 3 triangles. 540/180 = 3

Or, use Hero's formula:
Area = the square root of ( s (s-a) (s-b) (s-c) ) when a, b, and c are the three sides and s is the semi-perimeter ( 1/2(a+b+c) )

you mean Heron's? 

Quote from: ztrumpet on January 11, 2011, 05:32:30 pm

Or, use Hero's formula:
Area = the square root of ( s (s-a) (s-b) (s-c) ) when a, b, and c are the three sides and s is the semi-perimeter ( 1/2(a+b+c) )

you mean Heron's? 

This can be refered to as both Hero's and Heron's formula.  When I was in geometry, I remember reading ahead in my book to get this formula, and it said that both names are commonly used.

I think there also is a formula called the "Shoelace Formula" for finding the area of a triangle, but I never really investigated on how to go about using that formula. EDIT: Er, I guess the Shoelace Formula can be used to find the area of any polygon where the verticices are given ordered pairs as points.

or this formula?
V=A*B*sin[theta]

for clarification, i didnt post it as being a "heron's formula"
I love this formula because this pretty much get all the triangle's area.
EDIT: I messed around with trigs when I was 11 

I was in Honors math, and had an amazing teacher from 5th-8th. before that, i had had one other good math  teacher in fourth. So i've been pretty lucky.

Or, just do 4/3piR^3.....