Solution Step 0/0
A regular hexagon circumscribes a circle, which circumscribes another regular hexagon. The inner hexagon has an area of 3 square units. What is the area of the outer hexagon?
Explanations
A. Rotate the inner hexagon so that its corners touch the outer hexagon. B. Divide the inner hexagon into 6 equilateral triangles (solid lines). C. Divide them further into 3 identical isosceles triangles each (dotted lines).The 6 areas of the outer hexagon uncovered by the inner hexagon are equal in size to those isosceles triangles. Hence, the inner hexagon of 3 sq units consists of 18 isosceles triangles, while the outer one of 24 isosceles ones, or 4 sq units as result.
Check 3.5 sq units
Check 4 sq units
Check 4.5 sq units
Check 5 sq units
