Find the area of a parallelogram ABCD if three of its vertices are A (2, 4), B (2 + √3, 5) and C (2, 6).

Mid-point formula is given by,

(x, y) =

⇒ O (x, y) = = (2, 5)

Fourth vertex D is given by,

(x, y) =

⇒ (2, 5) =

⇒ 2 =

⇒ x₁ = 4 – 2 – √3 = 2 – √3

⇒ 5 =

⇒ y₁ = 10 – 5 = 5

⸫ D (x₁, y₁) = (2 – √3, 5)

Area of parallelogram ABCD = Area (ΔABC) + Area (ΔACD)

Area of triangle (x₁ (y₂ – y₃) + x₂ (y₃ – y₁) + x₃ (y₁ – y₂))

⸫ Area of ΔABC =

=

= sq. units

⸫ Area of ΔACD =

=

= sq. units

⸫ Area of parallelogram ABCD = (√3 + √3) sq. units

= 2√3 sq. units