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

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SUMMARY

The area of a triangle with non-intersecting vertices can be calculated by enclosing it within a tight rectangle. The area of the triangle is determined by subtracting the areas of the three right triangles formed outside the triangle from the area of the rectangle. This method is particularly useful when the triangle's vertices do not align with grid lines, necessitating the use of help lines to accurately estimate side lengths and areas. This approach is suitable for Elementary Students Math Olympiads.

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  • Understanding of basic geometry concepts, including area calculation.
  • Familiarity with right triangles and their properties.
  • Ability to visualize geometric shapes and their relationships.
  • Knowledge of grid systems and coordinate planes.
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  • Learn about coordinate geometry and its applications in area calculations.
  • Explore techniques for drawing geometric figures accurately.
  • Study the properties of triangles and their relationships to surrounding shapes.
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Elementary educators, math tutors, students preparing for Math Olympiads, and anyone interested in geometric problem-solving techniques.

Monoxdifly
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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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