Problem:
In the given figure hexagon ABCDEF is equiangular, ABJI and FEHG are squares with areas 18 and 32 respectively, △JBK is equilateral and FE=BC. What is the area of △KBC?
Answer Choices:
A. 62
B. 9
C. 12
D. 92
E. 32
Solution:
The area of the square ABJI is 18 and △KJB is equilateral, so KB=JB=18=32. The area of the square FEHG is 32, so BC=FE=32=42. Each interior angle of the hexagon is 120∘, so ∠KBC=360∘−60∘−90∘−120∘=90∘ and △KBC is a right triangle. Its area is 21⋅32⋅42=12.
