Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Triangles, Exercise 4: Challengers*

In the given figure, if $AY\perp ZY$ and $BY\perp XY$, such that $AY=ZY$ and $BY=XY$, then

The sides of a triangle are $2006 \mathrm{cm}, 6002 \mathrm{cm}$ and $m \mathrm{cm}$, where $m$ is a positive integer. The number of such possible triangles is

If $\angle ACB$ is a right angle and $AC=CD$ and $CDEF$ is a parallelogram. If $\angle FEC=10°$, the $\angle BDE$ equals

In the given figure, $\angle BCD=40°, \angle EDC=35°, \angle CBF=30°$ and $\angle DEG=40°$, then $\angle BAE$ equals

In the figure given below, two isosceles right-angled triangles, $DEF$ and $HGI$ are on the same base $\overline{DH}$. 

 $\overline{DH}$ is parallel to $\overline{FI}$.

If $DE=GH=9 \mathrm{cm}$ and $DH=20 \mathrm{cm}$, then the area of the quadrilateral $FEGI$ is