Question : Parallel sides of a trapezium are $26\;\mathrm{cm}$ and $40\;\mathrm{cm}$ and the area is $792\;\mathrm{cm^2}$. What is the value of the distance (in $\mathrm{cm}$) between parallel sides?

Option 1: $24\;\mathrm{cm}$

Option 2: $48\;\mathrm{cm}$

Option 3: $12\;\mathrm{cm}$

Option 4: $36\;\mathrm{cm}$

Question : In $\Delta\mathrm{ ABC,AD}$ and $\mathrm{AE}$ are bisectors of $\angle \mathrm{BAC}$ and $\angle \mathrm{BAD}$ respectively. If $\angle \mathrm{BAE}=30^{\circ}, \mathrm{AE}=9\;\mathrm{cm}$ and $\mathrm{EC}=15\;\mathrm{cm}$, what is the area (in$\;\mathrm{cm^2}$ ) of $\Delta \mathrm{CAE}$?

Option 1: $36$

Option 2: $54$

Option 3: $72$

Option 4: $216$

Question : In $\Delta \mathrm{ABC}$, a line parallel to side $\mathrm{BC}$ cuts the sides $\mathrm{AB}$ and $\mathrm{AC}$ at points $\mathrm{D}$ and $\mathrm{E}$ respectively and also point $\mathrm{D}$ divides $\mathrm{AB}$ in the ratio of $\mathrm{1 : 4}$. If the area of $\Delta \mathrm{ABC}$ is $200\;\mathrm{cm^2}$, then what is the area (in $\mathrm{cm^2}$) of quadrilateral $\mathrm{DECB}$?

Option 1: 192

Option 2: 50

Option 3: 120

Option 4: 96

Question : In the given figure, $\mathrm{DE} \| \mathrm{BC}$. If $\mathrm{AD}=5 \mathrm{~cm}, \mathrm{DB}=10 \mathrm{~cm}$, and $\mathrm{AE}=8 \mathrm{~cm}$, then $\mathrm{AC}$ is:

Option 1: 24 cm

Option 2: 32 cm

Option 3: 8 cm

Option 4: 16 cm

Question : For a triangle ABC, D and E are two points on AB and AC such that $\mathrm{AD}=\frac{1}{6} \mathrm{AB}$, $\mathrm{AE}=\frac{1}{6} \mathrm{AC}$. If BC = 22 cm, then DE is _______. (Consider up to two decimals)

Option 1: 1.33 cm

Option 2: 1.67 cm

Option 3: 3.67 cm

Option 4: 3.33 cm