The way to get started with this question is to sketch what’s described in the
question. A square of area 2.25 has sides each of length So the
perimeter of the square is 4(1.5) = 6. Since that’s also the perimeter of the
regular hexagon, and a regular hexagon has six equal sides, the length of each
side of the hexagon is 1.
Now the problem is one of finding the area of a regular hexagon of side length
- The fastest way to do that would be to use the formula, if you know it. If the
length of one side is s:
This formula is not one the test makers expect you to know—there’s always a
way around it—but if you like formulas and you’re good at memorizing them,
it can only help. Let’s proceed, however, as if we didn’t know the formula.
Another way to go about finding this area is to add a line segment or two to
the figure and divide it up into more familiar shapes. You could, for example,