To work out the perimeter of a square the formula is 4n. Using this 4x1=4. I need 8 slabs so that it goes all the way around the pond. I need four more. That makes 8. I will try using the formula 4n+4 to see how many slabs are needed.
It works for a square when the sides are 2x2 and 3x3.
4x2 = 8. 8+4 = 12
4x3 = 12. 12+4 = 16
The amount of slabs are correct.
I predict that the next size, 4x4 will have 20 slabs as four multiplied by four equals sixteen, add that to four and the number you get is twenty.
4x4 = 16
16+4 = 20
I was correct 20 slabs are needed.
Step by step
Pond 4x4m, needs slabs
round the side.
The perimeter is done
In slabs.
Corners are then
Added in.
This then makes 20 slabs. (Not to scale, slabs would be same size)
To prove my formula is correct I will show how many slabs are needed when the sides are from 1m – 14m.
As you can see the slabs needed add on four to each last one. If a person was to come into the garden centre and ask how many slabs they would need for a pond that has the length and width of 6m then the employees would know that 4x6 = 24 and then add four onto that would equal 28. The employee can then tell the customer that he/she will need 28 slabs.
I will now try to develop this knowledge so that the garden centre could sell slabs to accommodate those people with rectangular ponds.
1m
2m
There are 10 slabs.
To work out the perimeter of a rectangle the formula is 2l+2w.
2x2 = 4 2x1 = 2
4+2 = 6
Four more needed for the slabs, so 6+4 = 10. The amount of slabs
Formula
= 2l+2w
= 4lw+4
= Slabs needed.
These are just examples.
Using easy formulas and equations can help the garden centre to work out how many slabs are needed to go around a square or rectangular pond. The customer could give the employee a size of the shape and the employee can work it out, by working out the perimeter of the shape of the pond and then add four onto that.
The reason why four has to be added on to the answer of the perimeter is because the perimeter only works out the sides, the four to be added on is the corners.
By – Tim Royle