# 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.

## Most common method

Usually called "half of base times height", the area of a triangle is given by the formula below. where
b  is the length of the base
a  is the length of the corresponding altitude

You can choose any side to be the base. It need not be the one drawn at the bottom of the triangle. 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.

## Calculator

 ENTER ANY TWO VALUES Base clear Altitude clear Area clear

Use the calculator above to calculate the area of a triangle

Enter any two values and the other will be calculated. For example: enter the base and altitude and press 'Calculate'. The area will be calculated.

Similarly, if you enter the area and base, the altitude needed to get that area will be calculated.

## Methods for finding triangle area

 If you know: Use this Base and altitude "Half base times height" method All 3 sides Heron's Formula Two sides and included angle Side-angle-side method x,y coordinates of the vertices Area of a triangle- by formula (Coordinate Geometry) Area of a triangle - box method (Coordinate Geometry) The triangle is equilateral Area of an equilateral triangle

## Things to try

In the figure above, click on "freeze altitude". As you now drag point A, 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. Therefore, all the triangles you can create this way have the same area.