The diagram below represents an overhead view of a flat rectangular garden. The scale is one centimeter represents 2.5 meters. Work out the area of the garden in meters squared.
The keyword here is the word “scale” because it means that we know that this is a scale drawing. So what we can actually do is measure it and know that it’ll be in the right proportions.
Now to be able to actually calculate the area of the garden, what we want to do is actually find out the dimensions of our garden. And like I said, we’ll do this by first measuring each side. And when we actually measure the diagram, we can see that, actually, it’s got a length of eight centimeters and a width of four centimeters.
So now what we can do is actually think about, right, how to convert each of these into meters. And the reason we want to do that is because we want the area of the garden in meters squared. Well, we know that one centimeter is equal to 2.5 meters.
Well, therefore, if we want to actually find out what four centimeters is going to be, well we actually multiply it by four because four centimeters is four times bigger than one centimeter. So therefore, we’ve got to do the same to the 2.5 meters. So if we multiply this by four, we get 10 meters. So therefore, we can say that four centimeters is gonna be equal to 10 meters.
And then we can move on to eight centimeters. And to get to eight centimeters from four centimeters, well we’re actually gonna double it or multiply it by two. So therefore, we can actually do this to the 10 meters as well. And when we do this, we get a length of 20 meters. So great, we can actually write that next to the eight centimeters like we’ve done here. So we now know that the real dimensions of our garden are actually 20 meters by 10 meters.
Well, the alternative method we could’ve also used was actually could have been to multiply the four, from the four centimeters, by 2.5. And that’s cause we knew that one centimeter equal to 2.5 meters. And four multiplied by 2.5 gives us 10. So then we could’ve done the same with the eight centimeters. So we do eight multiplied by 2.5 would’ve given us 20. So again, would’ve got us our 20 meters. So great, we’ve actually found the dimensions.
Now what I need to do is actually work out the area. Well, to work out the area of a rectangle, we have the formula which is that area is equal to the length multiplied by the width. So therefore, in our case, the area is gonna be equal to 20 multiplied by 10. That’s because we’re using the real length and the real width. And we’ve got 20 meters as the real length and 10 meters as the real width.
And when we do this, we get the result from 20 multiplied by 10, which is 200. So therefore, we can say that the area of the garden in meters squared is 200 meters squared.
Well, it’s actually worth mentioning, even though we’ve got the answer as 200 meters squared, a common error that students make. So if we thought, well, let’s find out the area of the rectangle first, we do eight multiplied by four, which would give us 32. And then we could do 32 multiplied by 2.5, which would just give us 80. So wouldn’t this be correct?
Well, the answer is no, because actually the answer is 200 meters squared, not 80 meters squared. But we’ve done the right things. We’ve multiplied eight by four to find the area, and then we’ve multiplied it by the scale factor, which is 2.5. Well, in fact, if we wanted to use this method, we’d have to multiply by 2.5 squared. And the reason that is is because actually this is an area. 2.5 is a scale factor for the actual length or the dimensions. But with an area, we’re multiplying one dimension by another dimension. So therefore, we have to multiply it by a scale factor squared. So if we did 32 multiplied by 2.5 squared, that would give us the 200 meters squared that we’re looking for. So be careful for this kind of error.