A triangle ABC is specified on the coordinate plane. Find its area if it is known that A (-1; -3), B (-3; 3), C (3; 5).

Generally speaking, there are several ways to solve this problem, for example, you can first calculate the lengths of the sides of a triangle, after which you can apply Heron’s formula and calculate the area. If a triangle is specified on the coordinate plane (more precisely, the coordinates of its vertices are given), then the area of ​​the triangle S is very easy to calculate using the formula S = ½ * | (x1 – x3) * (y2 – y3) – (x2 – x3) * (y1 – y3) |, where A (x1; y1), B (x2; y2) and C (x3; y3) are the coordinates of the vertices of the triangle ABC.
We have S = ½ * | (–1 – 3) * (3 – 5) – (–3 – 3) * (–3 – 5) | = ½ * | (–4) * (–2) – (-6) * (–8) | = ½ * | 8 – 48 | = ½ * 40 = 20.
Answer: 20.