Question : In a triangle, ABC, P, and Q are points on AB and AC, respectively, such that AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, and CQ = 4.5 cm. If the area of $\triangle \mathrm{APQ}$ is 12 cm², then find the area of BPQC.

 

Option 1: 192 cm²

Option 2: 182 cm²

Option 3: 190 cm²

Option 4: 180 cm²

Question : If $\triangle A B C \sim \triangle D E F$, and $B C=4 \mathrm{~cm}, E F=5 \mathrm{~cm}$ and the area of triangle $A B C=80 \mathrm{~cm}^2$, then the area of the $\triangle DEF$ is:

Option 1: 169 cm²

Option 2: 80 cm²

Option 3: 144 cm²

Option 4: 125 cm²

Question : $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are similar triangles and their areas are 49 cm² and 144 cm² respectively, If $EF$ = 16.80 cm, then find $BC$.

Option 1: 7.5 cm

Option 2: 9.8 cm

Option 3: 8.7 cm

Option 4: 11.4 cm

Question : In trapezium $ABCD$, $AB \parallel CD$ and $AB = 2CD$. Its diagonals intersect at $O$. If the area of $\triangle AOB=84\;\mathrm{cm^2}$ then the area of $\triangle COD$ is equal to:

Option 1: 72 cm²

Option 2: 21 cm²

Option 3: 42 cm²

Option 4: 26 cm²

Question : If the surface area of a sphere is $1386 \mathrm{~cm}^2$, then its volume is:
(Take $\pi=\frac{22}{7}$ )

Option 1: 8451 cm³

Option 2: 4851 cm³

Option 3: 5418 cm³

Option 4: 4581 cm³

Question : The height of an equilateral triangle is $9 \sqrt{3} \mathrm{~cm}$. What is the area of this equilateral triangle?

Option 1:  $92 \sqrt{3} \mathrm{~cm}^2$

Option 2: $67 \sqrt{3} \mathrm{~cm}^2$

Option 3: $49 \sqrt{3} \mathrm{~cm}^2$

Option 4: $81 \sqrt{3} \mathrm{~cm}^2$