Let's set aside the fact that this is an
awful floorplan. How would you find furniture to fit this house?! <i class="em em-joy"></i>
If the two wall of the living room are parallel, then the kitchen and the (kitchen + living room + bath) are SIMILAR triangles. Similar triangles always have PROPORTIONAL sides. If we're given that the length of the left side of the kitchen is 30, and left side of the (kitchen + living room + bath) is 60 total, then the ratio of little triangle to big = 1 : 2. Thus, we can infer that the side lengths of the right-hand walls are 15 and 30:
If that's the case, then the bedroom (again, a
ridiculously shaped room) is an EQUILATERAL triangle of 30 : 30 : 30.
To find the area of any equilateral triangle, chop it into two 30-60-90 triangles.
If the base is 30, the height will be $$15\sqrt{3}$$
So, (1/2)(base)(height) = $$\left(\frac{1}{2}\right)\left(30\right)\left(15\sqrt{3}\right)$$
$$=225\sqrt{3}$$
The answer is
C. 
