| Math Open Reference | search | Home Index About Contact |
|
Area of a triangle
The number of square units it takes to exactly fill the interior of a
triangle.
Try this Drag the orange dots on each vertex
to reshape the triangle. The formula shown will recalculate the area using this method.
(If there is no image below, see support page.)
Most common methodUsually called "half of base times height", the area of a triangle is given by the formula below. (Also see Heron's Formula).
You can choose any side to be the base. The altitude must be the one corresponding to the base you choose. The altitude is the line perpendicular to the selected base from the opposite vertex. In the figure above, one side has been chosen as the base and its corresponding altitude is shown. Equilateral triangle area
In the special case of an
equilateral triangle, you can find the the area by the formula: where S is the length of any one side. If you know the three side lengthsIf you know the length of all three sides, it may be more convenient to use Heron's Formula to find the area of a triangle. For more on this, see Heron's Formula.If you know the coordinatesIf you know the x and y coordinates of the three vertices of a triangle, there two other ways to find its area:
Try this
In the figure above, drag the top of triangle carefully from left to right, but without moving it up or down.
It's a little tricky, but as you drag the vertex, notice that the area does not change.
The area is dependent on the base and height, and neither of them changes as you move the top vertex side-to-side.
Related triangle topicsGeneral
Triangle types
Triangle centersCongruence and SimilarityTriangle quizzes and exercises
(C) 2007 Copyright John Page
|
