Question : The area of the triangle formed by the graph of the straight lines $x-y=0$, $x+y=2$, and the $x$-axis is:

Option 1: 1 sq. unit

Option 2: 2 sq. units

Option 3: 4 sq. units

Option 4: 5 sq. units

Question : What is the area (in sq. units) of the triangle formed by the graphs of the equations $2x + 5y - 12=0, x + y = 3,$ and $y = 0$?

Option 1: 3

Option 2: 2

Option 3: 5

Option 4: 6

Question : A is the centre of a circle whose radius is 8 units, and B is the centre of a circle whose diameter is 8 units. If these two circles touch externally, then the area of the circle with diameter AB is:

Option 1: $36\pi$ sq. units

Option 2: $64\pi$ sq. units

Option 3: $144\pi$ sq. units

Option 4: $256\pi$ sq. units

Question : If for an isosceles triangle, the length of each equal side is $a$ units and that of the third side is $b$ units, then its area will be:

Option 1: $\frac{1}{4}\sqrt{4b^{2}-a^{2}}$ sq. units

Option 2: $\frac{a}{2}\sqrt{2a^{2}-b^{2}}$ sq. units

Option 3: $\frac{b}{4}\sqrt{4a^{2}-b^{2}}$ sq. units

Option 4: $\frac{b}{2}\sqrt{a^{2}-2b^{2}}$ sq. units

Question : The perimeter of a rhombus is $2p$ units, and the sum of the lengths of the diagonals is $m$ units. The area of the rhombus is:

Option 1: $\frac{m^{2}p}{4}$ sq. units

Option 2: $\frac{mp^{2}}{4}$ sq. units

Option 3: $\frac{m^{2} - p^{2}}{4}$ sq. units

Option 4: $\frac{p^{2} – m^{2}}{4}$ sq. units