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Altitude of a triangle formula
A triangle’s altitude or height is nothing but a perpendicular which we draw from the triangle’s vertex to its opposite face. As triangles include three sides, anyone can draw three altitudes within a triangle.
Different types of triangles portray different types of altitudes. The area of a triangular figure can be evaluated if you know its altitude. Another term for altitude is the height which is marked by the alphabet ‘h’.
What is the altitude of a triangle formula?
The fundamental formula that we implement to get the area of any triangle is: Total area = ½ x height x base. Here, height is nothing but the triangle’s altitude. From this formula only, you will be able to churn out the formula for evaluating the altitude of any triangle.
Altitude = (area x 2)/ base
In the next portion, we will see how you can calculate the height of an equilateral triangle, scalene triangle, isosceles triangle, and even a right-angled triangle.
Equilateral triangle | h = (a √3)/2 |
Scalene triangle | h = [2√s(s-a)(s-c)(s-b)]/b |
Isosceles triangle | h = √a2 – b2/4 |
Right-angled triangle | h = √x2+y2 |
Difference between height and median of a triangle
Although both the height and median of a triangle start from the vertex and end on the opposite face of a triangle, we must not use them synonymously.
Height or altitude | Median |
It is the perpendicular length from the triangular base to its opposite vertex. | It is a line segment starting from one of the vertices and ending on the opposite face. |
Sometimes height can even be outside a triangle. | Median always stays inside a triangle. |
It divides the triangle into equal halves. | Median does not equally divide a triangle. |
The common point where three heights of any triangle meet is defined as the orthocenter. | The common point where three medians of any triangle meet is defined as the centroid. |
Solved Examples
A triangle’s three sides are x = 3, y = 6 and z = 7 respectively. Determine its height.
Ans: From the problem it is easy to conclude that the given triangle is scalene in nature because each side has a different length.
Therefore, the height will be: [2√s(s-x) (s-z) (s-y)]/y
Here s is the semi perimeter.
s = (x+y+z)/2 = (3+6+7)/2 = 8 units
Therefore, h = [2√8(8-3) (8-7) (8-6)]/6
h =2.981 units
What is the height of the equilateral triangle who’s each side measures 8 cm.
Ans: Each side of this triangle measures 8 cm.
Therefore, the height or altitude = (a √3)/2 = (8√3)/2 cm = 4√3 cm
