Question

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

• A. 25.4
• B. 20.5
• C. 24.5
• D. none of these

Answer 1

The correct option is C

24.5

Let A, B, C, D be the points (-4, 2), (1, -1), (4, 1) and (2, 5) respectively.

Then the area of the quadrilateral ABCD $=\frac{1}{2}(-4\times -1-2\times 1+1\times 1-4\times -1+4\times 5-2\times 1+2\times 2\times -5\times -4)$
$=\frac{1}{2}(4-2+1+4+20+4+20)$
$=\frac{49}{2}=24.5$ squre units.
NOTE: Area of quadrilateral $=\frac{1}{2}(x_1{y}_2-x_2{y}_1)+(x_2{y}_3-x_2{y}_3)+(x_3{y}_4-x_4{y}_3)+(x_4{y}_1-x_1{y}_4))$