MHB Calculate Area of Triangle ABC

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The discussion focuses on calculating the area of Triangle ABC formed by points A(3, 4), B(8, 5), and C(7, 8) using a specific formula. The formula provided appears to have some typos, and an alternative method for calculating the area is suggested, which involves a different expression derived from the coordinates. Participants agree that the problem is straightforward, emphasizing a plug-and-chug approach to find the area. The conversation highlights the importance of correctly applying the formula and ensuring all variables are accurately represented. Overall, the area calculation process is clarified, with attention drawn to potential errors in the original formula.
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Point A(3, 4), point B(8, 5) and point C(7, 8) are located in quadrant 1 and form Triangle ABC.

Note:

Point A(a, b)
Point B(c, d)
Point C(e, f)

Find the area of Triangle ABC using the formula below.

A = (1/2)(a*d - c*b + c*e - e*d + e*b - a*e)

I think this is just a plug and chug problem. It looks tricky but in reality, it's not that bad.

I see it this way:

a = 3
b = 4
c = 8
d = 5
e = 7
f = 8

I plug the values of a through e (not including f) into the formula to calculate the area of Triangle ABC. Am I right?
 
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As you can find derived here:

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

we have:

$$A=\frac{1}{2}\left|(x_3-x_1)(y_2-y_1)-(x_2-x_1)(y_3-y_1) \right|$$

and putting this in terms of the given coordinates, we have:

$$A=\frac{1}{2}\left|(e-a)(d-b)-(c-a)(f-b) \right|$$

$$A=\frac{1}{2}\left|-ad+af+bc-be-cf+de \right|$$

Change the signs to match your formula:

$$A=\frac{1}{2}\left|ad-af-bc+be+cf-de \right|$$

Thus, I would posit that the formula you have been given has a few typos in it. :D
 
MarkFL said:
As you can find derived here:

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

we have:

$$A=\frac{1}{2}\left|(x_3-x_1)(y_2-y_1)-(x_2-x_1)(y_3-y_1) \right|$$

and putting this in terms of the given coordinates, we have:

$$A=\frac{1}{2}\left|(e-a)(d-b)-(c-a)(f-b) \right|$$

$$A=\frac{1}{2}\left|-ad+af+bc-be-cf+de \right|$$

Change the signs to match your formula:

$$A=\frac{1}{2}\left|ad-af-bc+be+cf-de \right|$$

Thus, I would posit that the formula you have been given has a few typos in it. :D

I made a few typos. Thanks.
 
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