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:
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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: \[ A = \frac{1}{2} \times b \times h \]
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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: \[ A = \sqrt{s(s - a)(s - b)(s - c)} \]
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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: \[ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
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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!