If `Δ ` denote the area of any triangle with semi-perimeter , then

Options

A. `Δ
lt(s^(2))/2`
B. `Δ
gt(s^(2))/4`
C. `Δ
lt(s^(2))/4`
D. `Δ
lts^(2)`

Explanation

To solve the problem, we need to establish the relationship between the area of a triangle (Δ) and its semi-perimeter (s). The semi-perimeter \( s \) is defined as:

\[ s = \frac{a + b + c}{2} \]

where \( a, b, c \) are the lengths of the sides of the triangle. We will use the formula for the area of a triangle in terms of its semi-perimeter and its sides, known as Heron's formula, which states:

...