Let us find the area of quadrilateral region formed by the line joining four given points each.

(1, 4), (–2, 1), (2, –3), (3, 3)

Let the points be A (1, 4), B (-2, 1), C (2, –3) and D (3, 3)

Plot the points we get the quadrilateral as shown

Divide the quadrilateral in two triangles by joining points A and C thus by observing figure we can conclude that

area(ABCD) = area(ΔABC) + area(ΔACD)

let us find area(ΔABC)

vertices are

A = (x₁, y₁) = (1, 4)

B = (x₂, y₂) = (-2, 1)

C = (x₃, y₃) = (2, -3)

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

Substituting values

⇒ area(ΔABC) = × [1(1 – (-3)) + (-2)(-3 – 4) + 2(4 – 1)]

⇒ area(ΔABC) = × [4 + 14 + 6]

⇒ area(ΔABC) = × 24

⇒ area(ΔABC) = 12

⇒ area(ΔABC) = 12 unit²

Let us find area(ΔACD)

Vertices are

A = (x₁, y₁) = (1, 4)

C = (x₂, y₂) = (2, -3)

D = (x₃, y₃) = (3, 3)

⇒ area(ΔACD) = × [1(-3 – 3) + 2(3 – 4) + 3(4 – (-3))]

⇒ area(ΔACD) = × [(-6) + (-2) + 21]

⇒ area(ΔACD) = × 13

⇒ area(ΔACD) = 6.5 unit²

Thus, area(ABCD) = area(ΔABC) + area(ΔACD)

⇒ area(ABCD) = 12 + 6.5

⇒ area(ABCD) = 18.5 unit²

Therefore, area of quadrilateral region is 18 unit²