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Course: Geometry (all content)>Unit 7

Lesson 6: Area of shapes on grids

Area of a triangle on a grid

Learn how to calculate the area of a triangle on a grid. Created by Sal Khan.

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• I'm not sure I understand how i'm supposed to find the area of the triangle. Can some one help me PLZ.
• the height times width then divide it in two
• I always thought that you were supposed to multiply the base and height, and then you divide that number by two. Is that still a good method?
• Yes that is how my teacher tought me yesterday
• If you multiply 1/2 to the base and the height What do you do?
• How do you know what the base or height is? Couldn't it be any side?
• Yes, it can be any side you choose. Just be sure that the base is perpendicular to the height: b⟂h
• What if you didn't have the height or the area?
• Then you split the triangle into two or more triangles and find the height and base of each of those triangles. Then you can find the area
• The second approach Sal takes only works because all of the vertexes of the triangle fall exactly on the edge of a unit box, right? Would you be able to use this method if the edges of the triangle weren't so exact?
• You may have to use Pythagorean Theorem or trig functions to find lengths of different sides of triangles along with possibly having to find where a line is perpendicular to another line and goes through a given point.
• Can the following formula be used to find the area of a triangle on a grid, given the coordinates?

area = Ax(By-Cy)+Bx(Ay-Cy)+Cx(By-Ay)/2

Ax = x coordinate for point A
Ay = y coordinate for point A
Bx = x coordinate for point B
By = y coordinate for point B
Cx = x coordinate for point C
Cy = y coordinate for point C

https://www.mathopenref.com/coordtrianglearea.html
• the pink triangle is exact copy of the shaded triangle so we just need to take out the area of pink triangle.