Question

How to calculate area of a triangle

Answer 1

To calculate the area of a triangle, you can use several different methods depending on the information you have. Here are a few common formulas:

1. **Base and Height Formula**:
If you know the base (b) and the height (h) of the triangle, the area (A) can be calculated using the formula:
\[
A = \frac{1}{2} \times b \times h
\]

2. **Heron's Formula**:
If you know the lengths of all three sides of the triangle (a, b, c), you can use Heron's formula. First, calculate the semi-perimeter (s):
\[
s = \frac{a + b + c}{2}
\]
Then, the area (A) is given by:
\[
A = \sqrt{s(s - a)(s - b)(s - c)}
\]

3. **Using Coordinates**:
If you have the coordinates of the vertices of the triangle (x1, y1), (x2, y2), and (x3, y3), you can use the following formula:
\[
A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
\]

4. **Trigonometric Formula**:
If you know two sides and the included angle (θ), you can calculate the area using:
\[
A = \frac{1}{2} \times a \times b \times \sin(\theta)
\]
where \( a \) and \( b \) are the lengths of the two sides.

Choose the method that best fits the information you have!