144. Triangulation Rocks the Nation

Codeforces

IDCF10269144

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

You have a triangle with three points given in coordinates. Given this information, figure out the triangle's area. The points can be given in any order. To calculate the area of a triangle, you can use Heron's Formula, which is described below: Define $A$, $B$, and $C$ to be the lengths of the three sides of the triangle. Define $S$ to be equal to $frac(A + B + C, 2)$. Then, the area of the triangle is calculated as $sqrt(S (S -A) (S -B) (S -C))$. The input consists of three lines, each consisting of two space-separated integers $x$ and $y$: the coordinates of each point of the triangle. Output a single decimal number $a$: the area of the triangle, using Heron's Formula as described above. Do not round your answer. This triangle corresponds to the first example case: ## Input The input consists of three lines, each consisting of two space-separated integers $x$ and $y$: the coordinates of each point of the triangle. ## Output Output a single decimal number $a$: the area of the triangle, using Heron's Formula as described above. Do not round your answer. [samples] ## Note This triangle corresponds to the first example case:

**Definitions** Let $ P_1 = (x_1, y_1) $, $ P_2 = (x_2, y_2) $, $ P_3 = (x_3, y_3) \in \mathbb{R}^2 $ be the coordinates of the three vertices of the triangle. **Constraints** The coordinates are given as real numbers (integers in input, but treated as reals for computation). **Objective** Compute the area of the triangle using Heron’s Formula: 1. Compute side lengths: $$ A = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, \quad B = \sqrt{(x_3 - x_2)^2 + (y_3 - y_2)^2}, \quad C = \sqrt{(x_1 - x_3)^2 + (y_1 - y_3)^2} $$ 2. Compute semi-perimeter: $$ S = \frac{A + B + C}{2} $$ 3. Compute area: $$ \text{Area} = \sqrt{S(S - A)(S - B)(S - C)} $$

API Response (JSON)

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      "content": "You have a triangle with three points given in coordinates. Given this information, figure out the triangle's area. The points can be given in any order.\n\nTo calculate the area of a triangle, you can ...",
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