What is the perimeter of the hexagon?
A hard-level "Length" problem.3.14 is not a number to memorise — it was squeezed out. The inscribed hexagon shows π > 3; a circumscribed square shows π < 4. More sides, more accuracy.
GivenA regular hexagon fits exactly inside a circle of radius 6 cm / π = 3.14
Hints
- Draw lines from the centre to the six corners: the hexagon splits into six triangles.
- Take one of them. The two sides from the centre are both radii, so they are equal — and the angle at the centre is 360 ÷ 6 = 60°.
- Two equal sides with 60° between them make an equilateral triangle, so the third side is also 6 cm — the same as the radius.
- All six sides equal the radius, so the perimeter is 6 × 6 = 36 cm.
- One last thing, and it matters. The hexagon lies inside the circle, so its perimeter must be shorter than the circumference. And 36 is exactly 3 × the diameter (12 cm). So diameter × 3 < circumference — which is a proof that π is bigger than 3.
Answer 36cm
More "Length" problems
- a + b + c = ?
- What is the side of the square?
- How long is MN?
- How long is the rope?
- How long is the pole's shadow?
- How deep was the water?
Browse by idea
- Circles and sectors — multiply by π once, at the very end
- Write the same thing two different ways
- Back to why the formula works