Le Matou matheux: square roots

The bee's sagacity

Let's take a 1 cm² and compare the perimeter of each figure.

A square
with area 1 cm²

Its side is . The perimeter of a square with area 1 cm² is

An equilateral triangle
with area 1 cm²

Before calculating the side of this triangle, you have to express the area of this triangle, in terms of its side a. Click then

As the area is 1 cm², a = to the nearest mm
The perimeter of an equilateral triangle with area 1 cm² is about

A regular hexagon with area 1 cm²

This hexagon is made up of triangles with side a.

Thus the area of the regular hexagon with side a equals x

As the area is 1 cm², a = to the nearest mm
The perimeter of a regular hexagon with area 1 cm² is about

Among this three figures with area 1 cm² , which one has the perimeter which is the smallest?