Compute the number of vinyl tiles, measuring 25 cm each side, needed to tile a kitchen measuring 102 ft. by 18 ft. try not to round your intermediate calculations, as it will propagate into your final answer.

First understand that to fill a flat space is to fill up the area. therefore we are looking for the area of the rectangular kitchen. we could find the exact amount of pieces needed for the length and thebexaxt amount needed for the width and then multiply these by each other to fill the length and width, which is the area. or we can find the area and divide that by the size of the tile to determine how many will fit. They they both are simple so I can try both. they will give same answer and maybe one way will be easier to understand than the other.

ok I will do the first way mentioned finding how many for length and how many for width and multiply together to get the amount it takes to fill.
So we have 102 ft but the tiles are measured in cm. So we need to convert one of them to match the other. It does not matter which. ultimately it will be the same answer. I will convert the centimeters so i can deal with smaller numbers. The conversion for cm to inches is 1 inch per 2.54 cm and inch to feet is 1 ft per 12 inches. So we can do:
25 cm * 1/2.54 in/cm * 1/12 ft/in

It it says to wait to round so we can just combine this into a fraction and say
(25) / (2.54*12) ft

this tells us how much length each tile takes down it's its length and width.

We we know the length is 102 ft so we can divide that by the length of tile and get amount of pieces that fit. For width it's the same but use width length of 18 ft. so:
length pieces = (102 ft) / [(25) / (2.54*12) ft]
width pieces = (18 ft) / [(25) / (2.54*12) ft]

we then multiply the pieces together to get pieces for area.
area pieces = length pieces * width pieces

the answer is 2729.1 pieces

the other way we find area of kitchen which is length * width. we divide this by area of tile to see how many for.
area kitchen = 102 * 18 ft^2

we found length and width of time earlier so:
area tile = [(25) / (2.54*12)]^2 ft

answer is:
area kitchen / area tile

so answer is:[(102 * 18) / ([(25) / (2.54*12) ft]^2)

or
2729.11

same answers