SOLUTION: The points of the triangle are A(1, 10), B(8, 1), and C(13, 1). How do I find the area of this triangle?

Question 660121: The points of the triangle are A(1, 10), B(8, 1), and C(13, 1).
How do I find the area of this triangle?
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The points of the triangle are A(1, 10), B(8, 1), and C(13, 1).
How do I find the area of this triangle?
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There are several ways. You can find the length of 3 sides and use Heron's Law.
You can find 2 sides and the included angle, then Area = a*b*sin(angle)
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Do it like this.
A B C A
1 8 13 1
10 1 1 10
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Add the diagonal products starting upper left.
1*1 + 8*1 + 13*10 = 1 + 8 + 130 = 139
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Add the diagonal products starting lower left.
10*8 + 1*13 + 1*1 = 80 + 13 + 1 = 94
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The area is 1/2 the ABS of the difference
(139 - 94)/2 = 22.5 sq units
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That works for any polygon, and number of sides.
I think the coordinates have to be entered in order around the polygon.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
this is your triangle:

now find the area:
...where is the base (in your case ) and is the height
as you can see, we need to calculate using distance formula:

Solved by pluggable solver: Distance Formula to determine length on coordinate plane

The distance (d) between two points is given by the following formula:

Thus in our case, the required distance is

For more on this concept, refer to Distance formula.

so,
now, we need : as you can see from the graph, will be a vertical line from the point to the point whose coordinate is
since coordinate of the point is , wee will go units to get in
so,
now we can calculate

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