Find the area of a triangle ABC with vertices A (-2; 0) B (5; 4) C (2; -5)

Let us construct a triangle ABC in the coordinate system at the given points.

Let’s complete the rectangle BDME and determine its area.

ME = 2 + 5 = 7 cm, DМ = 4 + 5 = 9 cm.

Then Svdme = 7 * 9 = 63 cm2.

Let’s define the areas of right-angled triangles ABD, ACM and BCE.

Savd = 4 * 7/2 = 14 cm2.

Sasm = 5 * 4/2 = 10 cm2.

Sall = 9 * 3/2 = 13.5 cm2.

Then Savs = Svdme – Savd – Sasm – Sall = 63 – 14 – 10 – 13.5 = 25.5 cm2.

Answer: The area of the triangle ABC is 25.5 cm2.