MHB How Do I Find the Area of a Triangle with Non-Intersecting Vertices?

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To find the area of a triangle with non-intersecting vertices, one approach is to draw a rectangle around the triangle and estimate its side lengths. The area of the triangle can then be calculated by subtracting the areas of the three right triangles formed outside the triangle. However, if the triangle's vertices do not touch the rectangle, adjustments are necessary. A suggested method involves drawing a help line from one vertex downward to align with another vertex on the grid line. This technique allows for accurate area calculations by adding and subtracting the relevant right triangles.
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What's the area of the triangle? It's hard because the vertices aren't in the intersections of horizontal and vertical lines, so I have a hard time determining the side lengths, and it's also for Elementary Students Math Olympiads too.
 

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Hi Mr. Fly,

How about we draw a tight rectangle around the triangle and we estimate its side lenghts?
The area of the triangle is then the area of the rectangle minus the area of the three right triangles.
 
Klaas van Aarsen said:
Hi Mr. Fly,

How about a tight rectangle around the triangle and estimate its side lenghts?
The area of the triangle is then the area of the rectangle minus the area of the three right triangles.

But the vertices of the triangle don't even touch the rectangle, so I think it's not that easy.
 
Monoxdifly said:
But the vertices of the triangle don't even touch the rectangle, so I think it's not that easy.

Draw a rectangle that touches the vertices. It won't be on the grid lines - only parallel to them.

Alternatively we can draw a help line from A downward to a point D on the same grid line as C.
Now we can add and subtract the relevant right triangles that are aligned with the help lines.
 

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