Triangle Area Calculator

How to Calculate Triangle Area

The area of a triangle can be calculated using various methods depending on the known information. Here are the most common approaches:

Triangle Area Formulas

1. Base and Height Method: \( Area = \frac{1}{2} \times base \times height \)
2. Heron's Formula (Three Sides): \( Area = \sqrt{s(s-a)(s-b)(s-c)} \), where \( s = \frac{a + b + c}{2} \)
3. Two Sides and Included Angle: \( Area = \frac{1}{2} \times a \times b \times \sin(C) \)
4. Two Angles and One Side: \( Area = \frac{a^2 \times \sin(B) \times \sin(C)}{2 \times \sin(A)} \)

Calculation Steps

1. Identify the known values of the triangle (sides, angles, or height).
2. Choose the appropriate formula based on the available information.
3. Substitute the known values into the chosen formula.
4. Perform the calculations step by step.
5. Round the result to the desired number of decimal places if necessary.

Example Calculation

Let's calculate the area of a triangle with base 6 units and height 4 units using the base and height method.

1. Given: base = 6 units, height = 4 units
2. Formula: \( Area = \frac{1}{2} \times base \times height \)
3. Substitute the values: \( Area = \frac{1}{2} \times 6 \times 4 \)
4. Calculate: \( Area = \frac{1}{2} \times 24 = 12 \) square units

Visual Representation

This diagram illustrates the triangle from our example, showing how the base and height are used to calculate the area.