Calculating the Area of a Triangle | Formulas for Various Scenarios

Formula for area of a triangle

The formula for the area of a triangle depends on the given information about the triangle

The formula for the area of a triangle depends on the given information about the triangle. There are different formulas to calculate the area based on the given sides and angles of the triangle.

Here are the formulas for finding the area of a triangle based on different scenarios:

1. If you know the length of the base and the height of the triangle, you can use the formula:
Area = (base * height) / 2

Here, the base is one side of the triangle, and the height is the perpendicular distance between the base and the vertex opposite to it.

2. If you know the lengths of all three sides of the triangle (a, b, c), you can use Heron’s formula:
Area = √(s(s-a)(s-b)(s-c))

Here, s represents the semi-perimeter of the triangle, which is calculated by adding all three sides and dividing by 2:
s = (a + b + c) / 2

3. If you know two sides of a triangle (a, b) and the included angle (θ) between them, you can use the formula:
Area = (1/2) * a * b * sin(θ)

In this formula, sin(θ) represents the sine of the included angle between the given sides.

4. If you know the lengths of two sides (a and b) and the angle (θ) between them, you can use the formula:
Area = (1/2) * a * b * sin(θ)

Again, sin(θ) represents the sine of the included angle between the given sides.

It is important to note that in order to use these formulas, you must have accurate measurements of the sides and angles of the triangle.

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