Area of Triangle

In this tutorial, we will discuss different scenarios based on the parameters available to compute the area of triangle. The parameters could be length of sides, angles, perimeter, altitude, etc.

We shall discuss following scenarios in detail.

  • Length of Three Sides are given.
  • Length of One Side and the two angles at its ends are given.
  • All the three angles and Perimeter is given.

We shall not consider any special cases of triangle based on equality in lengths or based on type of angle. For these special cases, follow these tutorials.

Compute Area of Triangle when Length of Three Sides are given

Consider the following triangle ABC, where we know the lengths of all three sides.

[figure]

When length of three sides are given, the formula to find area of the triangle is,

\[Area of \triangle ABC = \sqrt{p(p-a)(p-b)(p-c)} \]

where \(p = {a+b+c}\over 2\) i.e., half of perimeter of \(\triangle ABC)\

Example

Find Area of Triangle ABC whose length of sides are 5cm, 8cm and 6cm.

[figure]

Solution
Given a = 5cm
      b = 8cm
      c = 6cm

Area of triangle ABC =