The diagram shows a prism with the cross section of an irregular pentagon. On the grid below, draw the front elevation and the side elevation of the prism. Use a scale of one square to four metres.
Here’s a representation of our scale. Each square on our diagram represents four metres on the real diagram. Let’s begin by calculating the width of the front elevation. We are told that the width here is 24 metres. 24 divided by four is six. So that means that four multiplied by six is 24 metres. We can, therefore, scale up. One multiplied by six is six. So six squares must be equal to 24 metres.
Now, let’s consider the height. These measurements must be eight metres. Eight divided by four is two. So we can say that four multiplied by two must be eight. And we can, therefore, scale up to work out that two squares must be equal to eight metres.
Now, remember when we are looking at the shape from the front, we won’t see it in three dimensions. Actually to us, it will look like a rectangle with another rectangle on top of it. We need to work out the height of the rectangle at the top.
Since the total height of the prism is 14 metres and the height of the rectangle we’ve already taken into account is eight metres, this missing height can be found by subtracting eight from 14. It’s six. Scaling up from four metres to six metres is a little bit more complicated.
Remember though when we were trying to find out what we needed to do to scale from four to 24, we divided 24 by four. This time, we’ll divide six by four. And that gives us 1.5. So we can say that four multiplied by 1.5 is six. One multiplied by 1.5 is 1.5. So 1.5 squares or one and a half squares must be equal to six metres.
And we can now draw the front view of this prism. It has a width of 24 metres and a height in total of 14 metres, made up of eight metres and six metres.
Now, let’s consider the view from the side. We already worked out that eight metres is equal to two squares on our diagram. Now, let’s think about the width of the side elevation; it’s 16 metres. 16 divided by four is four. So we can say that four multiplied by four is 16. One multiplied by four is four. So that tells us that four squares must be equal to 16 metres.
Now, we have actually already worked out what 14 metres looks like on our diagram. But let’s recap a slightly different method. 14 divided by four is three and a half. So we can say that four multiplied by 3.5 is 14. One multiplied by 3.5 is 3.5. So 3.5 or three and a half squares is equal to 14 metres. And we can draw the side elevation of the prism as shown.
We can deduce that we’ve probably done this correctly. These two highlighted parts actually represent the same part of the prism. And we can see that in our front and our side elevation, they’re actually the same length. So we’ve probably done this correctly.
And we’re done. There’s the front and the side elevation of our prism.