Question

Find the area of quadrilateral formed by joining the points (- 4, 2), (- 1, 0), (4, 1) and (2, 5):

• A. 20
• B. 40
• C. 36
• D. 21 .5

Answer 1

The correct option is D 21 .5

1^st method: - The simplest way to find this is to put a rectangle around the given quadrilateral and then subtract off the areas of the right triangles that surround it. (See Figure) The area of the entire rectangle is 40, but after subtracting the areas of the 4 right triangles, whose areas are 5/2, 4, 9 and 3. we are left with an area of 21.5.

2^nd method: - Area of quadrilateral = {(x₁y₂ – x₂y₁) + (x₂y₃ – x₃y₂) + (x₃y₄ – x₄y₃) + (x₄y₁ – x₁y₄)}

= {( -4 x 0 – (- 1) x 2) + (- 1 x 1 – 4 x 0) + (4 x 5 – 2 x 1) + (2 x 2 – (-4)x 5)}=21.5