The intersection between x-2y-3=0 and 2x+y-11=0 is indeed a right angle. Their slopes are negative reciporcals of each other.

First, solve for the intersections of your 3 lines by solving simultaneous equations.

Then use the distance formula to determine the lengths of the two legs of your right triangle.

Then use A=1/2 bh, where b and h are your two legs.