Mastering the Triangle Area Formula: Base and Height, Heron’s Formula, Included Angle and Shoelace Method

area of a triangle

The formula to calculate the area of a triangle depends on the information given

The formula to calculate the area of a triangle depends on the information given. There are different cases to consider:

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

Area = (1/2) * base * height

In this case, the base is the length of the bottom side of the triangle, and the height is the perpendicular distance from the base to the top vertex.

2. If you know the lengths of all three sides of the triangle, you can use Heron’s formula:

Area = √[s(s – a)(s – b)(s – c)]

where “s” is the semiperimeter of the triangle (s = (a + b + c)/2), and “a,” “b,” and “c” are the lengths of the sides.

3. If you know the lengths of two sides and the included angle between them, you can use the formula:

Area = (1/2) * a * b * sin(theta)

where “a” and “b” are the lengths of the sides, and “theta” is the angle between them.

4. If you know the coordinates of the vertices of the triangle, you can use the Shoelace formula:

Area = (1/2) * |(x1y2 + x2y3 + x3y1) – (x2y1 + x3y2 + x1y3)|

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices of the triangle.

Remember to use the appropriate formula based on the information given in the problem.

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