Question

Area of the quadrilateral formed by the points $(1,1),(0,1),(0,0)$ and $(1,0)$ is

• A. $3$ sq.units
• B. $2$ sq.units
• C. $4$ sq.units
• D. $1$ sq.units

Answer 1

The correct option is D $1$ sq.units

Consider the given points.

$(1,1),(0,1),(0,0)$ and $(1,0)$

We know that the area of the quadrilateral

$=\frac{1}{2}\left[\right(x_1{y}_2+x_2{y}_3+x_3{y}_4+x_4{y}_1)-(x_2{y}_1+x_3{y}_2+x_4{y}_3+x_1{y}_4\left)\right]$

where $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$ are the vertices of the quadrilateral

So,

Area $=\frac{1}{2}\left[\right(1\times 1+0\times 0+0\times 0+1\times 1)-(0\times 1+0\times 1+1\times 0+1\times 0\left)\right]$

$=\frac{1}{2}\left[\right(1+0+0+1)-(0+0+0+0\left)\right]$

$=\frac{1}{2}[2-0]$

$=\frac{1}{2}\times 2=1sq.units$

Hence, this is the answer.