Area of Triangle

Q. In the circle given below, let $OA=1$ unit, $OB=13$ unit and $PQ\perp OB.$ Then, the area of the triangle $PQB$ (in square units) is :

1. $26\sqrt{3}$
2. $24\sqrt{2}$
3. $24\sqrt{3}$
4. $26\sqrt{2}$

Q. From a square with sides of length $5$ unit, triangular pieces from the four corners are removed to from a regular octagon. Then the area removed is
(correct answer + 1, wrong answer - 0.25)

1. $25(3+\sqrt{2})\text{sq. units}$
2. $25(3+2\sqrt{2})\text{sq. units}$
3. $25(3-2\sqrt{2})\text{sq. units}$
4. $25(3-\sqrt{2})\text{sq. units}$

Q. The angles $A,B$ and $C$ of a triangle $ABC$ are in $A.P.$ and $a:b=1:\sqrt{3}.$ If $c=4\text{cm}$, then the area (in sq.cm) of this triangle is:

1. $4\sqrt{3}$
2. $2\sqrt{3}$
3. $\frac{4}{\sqrt{3}}$
4. $\frac{2}{\sqrt{3}}$