Question

Two sides of a square lie on the lines $x+y=1$ and $x+y+2=0$. What is its area ?

Answer 1

The equations of parallel sides of the square are $x+y-1=0$ and $x+y+2=0$.

Therefore, Length of the side of the square = Distance between parallel side $=\frac{|c_1-c_2|}{\sqrt{a_1^2+b_1^2}}$$=\frac{|2-(-1)|}{\sqrt{1^2+1^2}}=\frac{3}{\sqrt{2}}$

Hence, area of the square = $(side{)}^2=\frac{9}{2}sq.units$