Can we apply Heron's formula for Right-angle triangle,equilateral triangle and isoceles

Dear student,

Yes, Heron's formula can be applied to find the area of an isosceles triangle, right triangle and equilateral triangle.
Taking an example to find the area of an isosceles triangle;
Suppose we have an isosceles triangle in which equal sides of an isosceles triangle are 3 m and the third side of a triangle is 4 m.
So; length of the sides of triangle are a = b = 3 m and c = 4 m
Then perimeter of triangle = a + b + c = 3 + 3 + 4 = 10 m
So semi perimeter of triangle; s = $\frac{10}{2} = 5 \mathrm{m}$
Using Heron's formula we have;
Area of an isosceles triangle = $\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$
$$\begin{gathered} = \sqrt{5\left(5-3\right)\left(5-3\right)\left(5-4\right)} \\ = \sqrt{5\times 2\times 2\times 1} \\ = \sqrt{20} \\ = 2\sqrt{5} {\mathrm{m}}^2 \end{gathered}$$
So we can apply Heron's formula to find the area of an isosceles triangle.
Similarly we can apply Heron's formula to find the area of equilateral and right triangle also.


Regards