Calculating the Area of a Triangle | Formulas and Methods Explained

Area of triangle

The area of a triangle is the measure of the surface enclosed within its three sides

The area of a triangle is the measure of the surface enclosed within its three sides.

To find the area of a triangle, you can use different methods depending on the information you have.

1. If you know the base and the height of the triangle:
– The formula for the area is: Area = (base * height) / 2.
– The base is one of the sides of the triangle, and the height is the perpendicular distance from the base to the opposite vertex.

2. If you know the lengths of all three sides (using Heron’s formula):
– Let’s say the sides of the triangle have lengths a, b, and c.
– Calculate the semi-perimeter of the triangle: s = (a + b + c) / 2.
– Then, use the formula: Area = √(s * (s – a) * (s – b) * (s – c)).
– This formula is derived from Heron’s formula, which can be used for all types of triangles (scalene, isosceles, or equilateral).

3. If you know the coordinates of the three vertices of the triangle (using the Shoelace formula):
– Let’s say the coordinates of the vertices are (x₁, y₁), (x₂, y₂), and (x₃, y₃).
– Calculate the area using the formula: Area = 1/2 * |(x₁y₂ + x₂y₃ + x₃y₁) – (x₂y₁ + x₃y₂ + x₁y₃)|.
– The absolute value ensures the result is positive, and the 1/2 is included to calculate the area correctly.

Remember, when using any of these methods, it is important to use the correct units (e.g., square units) for the length and area measurements.

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