Find the area of triangular region with vertices given below.

(1, 2), (3, 0) and origin

Area of triangle is given by formula

Area = × [x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)]

Where (x₁, y₁), (x₂, y₂) and (x₃, y₃) are vertices of triangle

Here,

(x₁, y₁) is (1, 2)

⇒ x₁ = 1 and y₁ = 2

(x₂, y₂) is (3, 0)

⇒ x₂ = 3 and y₂ = 0

(x₃, y₃) is origin which is (0, 0)

⇒ x₃ = 0 and y₃ = 0

Hence substituting values in formula for area we get

Area = × [1(0 – 0) + 3(0 – 2) + 0(2 – 0)]

Area = × [0 + (-6) + 0]

Area = -3

As area cannot be negative

Area = 3 unit²