heron's formula is applicable for all triangles or not Related: Heron...
Yes, but it is easy to use 1/2bh when base and height are given and it is easy to use √3a×a/4 for equilateral triangles.
heron's formula is applicable for all triangles or not Related: Heron...
Applicability of Heron's Formula
Heron's formula is applicable for all triangles, regardless of their type or shape. It can be used to find the area of any triangle as long as you have the lengths of all three sides.
Explanation of Heron's Formula
- Heron's formula is a mathematical formula used to calculate the area of a triangle when the lengths of all three sides are known.
- The formula is given by: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle given by s = (a + b + c)/2, and a, b, c are the lengths of the three sides.
- This formula is derived from Heron's proof of the same, which involves using the Pythagorean theorem and trigonometric identities.
Usefulness of Heron's Formula
- Heron's formula is particularly useful when the triangle is not a right-angled triangle and traditional methods like the base-height formula cannot be used.
- It is also helpful when you only have the lengths of the sides of the triangle and not the height or any angles.
Visual Representation
Heron's formula provides a straightforward and efficient way to find the area of any triangle, making it a valuable tool in geometry and trigonometry.
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