Different Formulas to Calculate the Area of a Triangle: Base and Height, Sides Lengths, and Coordinates of Vertices

Area of a triangle

The area of a triangle can be calculated using different formulas depending on the given information

The area of a triangle can be calculated using different formulas depending on the given information.

1) If you know the base and height of the triangle:
The formula to calculate the area of a triangle is:
Area = (base * height) / 2

2) If you know the lengths of all three sides of the triangle:
You can use Heron’s formula to calculate the area of a triangle:
Area = √(s * (s – a) * (s – b) * (s – c))
where “s” represents the semi-perimeter of the triangle, which is calculated by adding the lengths of all three sides and dividing by 2. “a,” “b,” and “c” represent the lengths of the three sides of the triangle.

3) If you know the coordinates of the vertices of the triangle:
You can use the shoelace formula (also known as Gauss’s area formula) to calculate the area of a triangle:
Area = 1/2 * |(x1y2 + x2y3 + x3y1) – (x2y1 + x3y2 + x1y3)|
where (x1, y1), (x2, y2), and (x3, y3) represent the coordinates of the three vertices of the triangle.

Remember to use the appropriate formula based on the given information to calculate the area of a triangle accurately.

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