To understand how to calculate the area of a triangle, you first need to know what is a triangle. Triangle, also known as a trigon, is a three-sided closed figure. The word is taken from the Greek word ‘tri’, which means three. Therefore, deriving the literal meaning of a three-angled figure is known as a triangle. Triangles are classified into the following based on two properties - the length of the sides and the degree of angles. Read below to find out more details about types of triangles:
According to the length of the sides:
According to the degree of angles:
Heron’s formula is often referred to as Hero’s formula, which was named after the great Hero of Alexandria. This formula is beneficial in calculating the area of any three-sided figure if all the lengths of that figure are well defined.
To apply Heron’s Formula, we must first determine the value of the semi-perimeter. It is denoted by the symbol ‘s’. The semi-perimeter is defined as the sum of all three lengths of the triangle divided by 2.
For example, let us consider a triangle QPR with lengths k, l, and m.
Therefore, s = (k + l + m)/2
Next, we substitute the value of ‘s’ in Heron’s main formula, which is stated as:
Area of a triangle = √ s (s-k) (s-l) (s-m)
We saw that a triangle format might be used to determine the area of specific triangles. But the computation of height would not be easy for a triangle with the sides specified. So we rely on Heron's Formula for the same reason to compute the triangular area with uniform lengths. Heron’s formula is very beneficial in higher studies, including engineering.
You may also want to know 'how to find perimeter of the triangle'.
Type of Triangle | Formula for Area |
Standard triangle (with height) | ½ x base x height |
Standard triangle with three sides given (Scalene triangle) | Using Heron’s Formula = √ s (s-k) (s-l) (s-m) |
Isosceles triangle | ½ x base (non-equal side) x height (perpendicular drawn from the vertex to the base) |
Equilateral triangle | (√3)/4 × s2, where s is the sides of the triangle |
We can also determine the area of any triangle if any two sides and the angle between those particular two sides are given. Let us assume a triangle KLM with a length of the side k, l, and m, respectively. Let the angle associated be A, B, and C; therefore, an area of the triangle is calculated using one of the three formulas :
Click here to know more about Trigonometric functions (Sine, Cosine, Tangent, Secant, Cosecant and Cotangent).