Calculate the area of a triangle using base and height or Heron's formula.
Choose a method to calculate the area of a triangle.
Base and Height Method:
The area of a triangle using base and height is calculated with the formula:
\[ \text{Area} = \frac{1}{2} \times b \times h \]
Where:
For example, if \( b = 6 \) units and \( h = 4 \) units, then \( \text{Area} = \frac{1}{2} \times 6 \times 4 = 12 \) square units.
Heron's Formula:
When the lengths of all three sides (\( a \), \( b \), \( c \)) are known, the area is calculated using:
\[ \text{Area} = \sqrt{s(s - a)(s - b)(s - c)} \]
Where \( s \) is the semi-perimeter:
\[ s = \frac{a + b + c}{2} \]
For example, if \( a = 3 \), \( b = 4 \), \( c = 5 \), then \( s = \frac{3 + 4 + 5}{2} = 6 \), and \( \text{Area} = \sqrt{6(6-3)(6-4)(6-5)} = \sqrt{6 \times 3 \times 2 \times 1} = \sqrt{36} = 6 \) square units.