Find the area of triangular region with vertices given below.

(8, 9) (2, 6) and (9, 2)

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 (8, 9)

⇒ x₁ = 8 and y₁ = 9

(x₂, y₂) is (2, 6)

⇒ x₂ = 2 and y₂ = 6

(x₃, y₃) is (9, 2)

⇒ x₃ = 9 and y₃ = 2

Hence substituting values in formula for area we get

Area = × [8(6 – 2) + 2(2 – 9) + 9(9 – 6)]

Area = × [32 + (-14) + 27]

Area = × [32 + 13]

Area = × 45

Area = 22.5 unit²