Mastering Triangle Area Calculations | Formulas for Base and Height, Lengths of Sides, and Coordinate Coordinates

Area of a Triangle

The area of a triangle is the measurement of the region enclosed by the three sides of the triangle

The area of a triangle is the measurement of the region enclosed by the three sides of the triangle. It is expressed in square units (e.g., square centimeters, square inches, etc.). The formula to calculate the area of a triangle depends on the information given.

1. If the base and height of the triangle are known, you can use the formula:

Area = (base × height) / 2

The base is any of the sides of the triangle that is chosen as the bottom edge, and the height is the perpendicular distance from the base to the opposite vertex.

2. If the lengths of the three sides of the triangle are given, you can use Heron’s formula, which is suitable for any type of triangle:

Area = √(s × (s-a) × (s-b) × (s-c))

where ‘s’ denotes the semi-perimeter of the triangle, calculated as (a + b + c) / 2, and ‘a’, ‘b’, and ‘c’ represent the lengths of the sides.

3. If the coordinates of the vertices of the triangle are known, you can use the shoelace formula:

Area = 0.5 × |(x1y2 + x2y3 + x3y1) – (x2y1 + x3y2 + x1y3)|

In this formula, (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the three vertices of the triangle.

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

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