MHB What is the area of a triangle given (2, 3), (4, 5), and (6, 7)?

[mathdad]

Given (2, 3), (4, 5), (6, 7), find the area using the formula below.

Note: (a, b) (c, d) (e, f)

a = 2
b = 3

c = 4
d = 5

e = 6
f = 7

A = (1/2)[(ad - cb) + (cf - ed) + (eb - af)]

Just plug and chug, right?

 

[MarkFL]

Suppose you weren't given a formula into which you may "plug and chug"...can you outline a method you could use to find the area?

 

[mathdad]

1. Apply distance formula 3 times.

2. Heron's Formula

 

[skeeter]

Given (2, 3), (4, 5), (6, 7), find the area using the formula below.

Note: (a, b) (c, d) (e, f)

a = 2
b = 3

c = 4
d = 5

e = 6
f = 7

A = (1/2)[(ad - cb) + (cf - ed) + (eb - af)]

the area will be zero ... those three points are collinear

 

[mathdad]

Suppose you weren't given a formula into which you may "plug and chug"...can you outline a method you could use to find the area?

1. Apply distance formula 3 times.

2. Heron's Formula.

 

[MarkFL]

1. Apply distance formula 3 times.

2. Heron's Formula.

Yes, that's likely the quickest way to get the area without an explicit formula for the area of a triangle formed by 3 points in the plane. (Yes) I once posted a tutorial here on deriving a general formula:

http://mathhelpboards.com/math-notes-49/finding-area-triangle-formed-3-points-plane-2954.html

And it relies on the following derivation:

http://mathhelpboards.com/math-notes-49/finding-distance-between-point-line-2952.html

 

[mathdad]

Great information.