SOLUTION: if the vertices of a triangle are A (1,3) B (3,4) and C (1,-4) find its area.
A) 10
B) 7
C)9
D)12
E) 18
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Question 1101442: if the vertices of a triangle are A (1,3) B (3,4) and C (1,-4) find its area.
A) 10
B) 7
C)9
D)12
E) 18
Found 2 solutions by htmentor, Alan3354:
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The easiest way to solve is to draw a rectangle on the gridlines around the triangle as in the figure below.
Then the area of triangle ABC will be the area of the rectangle minus the area of the outer triangles BCD and ABE
From the figure, we see that the area of the rectangle is 8*2 = 16
The area of triangles BCD and ABE is 1*8 + 1/2*2 = 9
Therefore the area of the triangle ABC is 16 - 9 = 7
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
if the vertices of a triangle are A (1,3) B (3,4) and C (1,-4) find its area.
==========
Here's another method.
A B C A
1 3 1 1
3 4 -4 3
------------
Add the diagonal products starting at the upper left.
4 -12 + 3 = -5
---
Add the diagonal products starting at the lower left.
9 +4 -4 = 9
The difference is 14
The area is 1/2 that,
Area = 7 sq units
================
This methods works for ALL polygons, any number of sides.
The points must be in order around the polygon.
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