   SEARCH HOME Math Central Quandaries & Queries  Hi, We are laying a concrete slab in the shape of a regular hexagon with each side being 2m long. The slab will be 10cm thick. How much concrete will we need? Thank you ever so much! Hi again, Could you please tell me the distance from one side of a hexagon to the opposite side (diameter) if each section of the hexagon is 2m long? Thank you, kind regards, Mandy Mandy Hi Mandy,

The volume is the area of the hexagon times the thickness. If you look at the answer Sue gave to a question about the area of a hexagon you can apply it to your situation. You have a side length of a = 2 m and Pythagoras theorem gives a height of √3 = 1.7 m. Thus the area of the hexagon is

3a 1.7 = 6 1.7 = 10.4 sq m.

The thickness is 10 cm = 1/10 m and hence the volume of concrete you need is

10.4 1/10 = 1.0 cubic metres.

If you look at the answer Chris and Harley gave to another of the questions we received you will see that the relationship between the width W of a hexagon and the length of the side L (called a above) is

W = √3 L

Since you have L = 2 m the width will be

√3 2 = 3.5 m.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.