Use calculus to find area of triangle with given vertices
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To find the area of the triangle with vertices (0,0), (1,1) and (2,0), first draw a graph of that triangle. It is made up of the three lines y=0, y=x, and y=2-x. Now look at your graph:
Between the points x=0 and x=1 (i.e. the left half of the triangle) we want to find the area between y=x and y=0. For the right half of the triangle we need to find the area between y=2-x and y=0. Hence we compute:
Area = A(left) + A(right)
which is
The value of which is 1 square unit.
The most important thing is to always draw a picture first and use it to figure out what the equations of your lines are and in how many parts you need to split the triangle to compute the area.
Between the points x=0 and x=1 (i.e. the left half of the triangle) we want to find the area between y=x and y=0. For the right half of the triangle we need to find the area between y=2-x and y=0. Hence we compute:
Area = A(left) + A(right)
which is
The value of which is 1 square unit.
The most important thing is to always draw a picture first and use it to figure out what the equations of your lines are and in how many parts you need to split the triangle to compute the area.
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