The area enclosed within the curve $|x| + |y| = 1$ is

If the line $3x + 3y -24 = 0$ intersects the $x-$ axis at the point $A$ and the $y-$ axis at the point $B$, then the incentre of the triangle $OAB$, where $O$ is the origin, is

Let a triangle be bounded by the lines $L _{1}: 2 x +5 y =10$; $L _{2}:-4 x +3 y =12$ and the line $L _{3}$, which passes through the point $P (2,3)$, intersect $L _{2}$ at $A$ and $L _{1}$ at $B$. If the point $P$ divides the line-segment $A B$, internally in the ratio $1: 3$, then the area of the triangle is equal to

The vertex of a right angle of a right angled triangle lies on the straight line $2x + y - 10 = 0$ and the two other vertices, at points $(2, -3)$ and $(4, 1)$ then the area of triangle in sq. units is

The ends of the base of an isosceles triangle are at $(2a,\;0)$ and $(0,\;a).$ The equation of one side is $x=2a$ The equation of the other side is

A vertex of equilateral triangle is $(2, 3)$ and equation of opposite side is $x + y = 2,$ then the equation of one side from rest two, is