Question 1064651: What is the area of a triangle whose vertices are R(−4,2) , S(1,2) , and T(−5,−4)?
Found 2 solutions by KMST, Alan3354:
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! That triangle has a horizontal base with y=2.
The length of that base is RS=1-(-4)=1+4=5.
The height of the triangle is the vertical distance
from line y=2 to T(-5,-4).
That height is
2-(-4)=2+4=6.
The area of the triangle is
 .
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! What is the area of a triangle whose vertices are R(-4,2), S(1,2), and T(-5,-4)?
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You can find the 3 side lengths, then use Heron's Law.
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Or,
R S T R
-4 1 -5 -4
2 2 -4 2
Add the diagonal products starting at the upper left:
= -8 - 4 - 10 = -22
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Add the diagonal products starting at the lower left:
= 2 - 10 + 16 = 8
|-22 - 8| = 30
The area is 1/2 of that, = 15 sq units.
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This method works for any polygon, any # of sides.
The points have to be in order around the perimeter.
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