Altitude of a Triangle Formula
The perpendicular drawn from the vertex to the opposite side of the triangle is called the altitude of a triangle. Altitude of a Triangle Formula gives us the height of the triangle. The altitude of a triangle formula is interpreted and different formulas are given for different types of triangles. The altitude is used for the calculation of the area of a triangle.
What is the Altitude of A Triangle Formula?
The Altitude of a triangle Formula can be expressed as follows. Here the altitude is represented by the alphabet h. Further, we can also see below the different altitude of a triangle formulas for different triangles.
General formula for altitude of a triangle \((h)=\dfrac{2 \times \text{Area}}{\text{base}}\)
Observe the table to go through the formulas used to calculate the altitude (height) of different triangles.



\(h= \frac{2 \sqrt{s(sa)(sb)(sc)}}{b}\) Where a,b,c are the sides of the triangle, and s is the semi perimeter 
\(h= \frac{a\sqrt{3}}{2}\) Where a is a side of a triangle 
\(h= \sqrt{xy}\) where x and y are the length of segments of hypotenuse divided by altitude. 
\(h= \sqrt{a^2 \frac{b^2}{4}}\) where a and b are the side of a triangle 
Let us try out a few examples to know how to use Altitude of a Triangle Formula.
Solved Examples on Altitude of a Triangle Formula

Example 1: The area of a right triangular swimming pool is 72 sq. units. Find the length of the altitude if the length of the base is 9 units.
Solution: To find: The length of the altitude.
The area of a right triangular swimming pool = 72 sq. units(given)
\The length of the base = 9 unitsUsing Altitude of A Triangle Formula,
Altitude of A Triangle(h)= \(\frac{2\times\ Area}{base}\)
\(Altitude(h)= \dfrac{2\ \times\ 72}{9}\)
Altitude(h)= 16 units
Answer: The length of the altitude of a triangle is 16 units.

Example 2: Calculate the length of the altitude of a triangle drawn from vertex A. Whose semiperimeter is 12 feet and sides a,b.c are 9 feet, 7 feet, 8 feet respectively.
Solution: To find: Circumference of a park.
Semiperimeter= 12 feet (given)
Using Altitude of A Triangle Formula,
Altitude of the Triangle (h) = \(\dfrac{2 \sqrt{s(sa)(sb)(sc)}}{b}\)
Altitude(h)= \(\dfrac{2 \sqrt{12(129)(128)(127)}}{8}\)
Altitude(h)= \(\dfrac{2 \sqrt{12\ \times 3\ \times 4\ \times 5}}{8}\)
Altitude(h)= \(\dfrac{ 12\ \sqrt{5}}{4}\)
Altitude(h)= \(3\sqrt{5}\) feet
Answer: The length of the altitude of a triangle drawn from vertex A is \(3\sqrt{5}\) feet.