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[ASK] Area of a Triangle

Monoxdifly

Well-known member
Aug 6, 2015
271
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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Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,713
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.
 

Monoxdifly

Well-known member
Aug 6, 2015
271
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.
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,713
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.