Question

The sides of an $8\times 8$ square are cut by certain points into pieces of length $1$ and $7$, $2$ and $6$, $3$ and $5$ and $4$ and $4$ as shown in the figure above. The area of the quadrilateral determined by these four points are

• A. $28$
• B. $36$
• C. $48$
• D. $8$

Answer 1

The correct option is B $36$

Area of quadrilateral = Area of square - (Area of four triangles)
$=8\times 8-\left[\frac{1}{2}\times 1\times 4+\frac{1}{2}\times 4\times 5+\frac{1}{2}\times 3\times 6+\frac{1}{2}\times 2\times 7\right]=64-[2+10+9+7]=64-28=36sq.units$