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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
153–√153
So, (1/2)(base)(height) =
(12)(30)(153–√)(12)(30)(153)
=2253–√=2253
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