Lesson Video: Plans and Elevations | Nagwa Lesson Video: Plans and Elevations | Nagwa

# Lesson Video: Plans and Elevations Mathematics

In this video, we will learn how to find the front, top, and side views of a three-dimensional shape and identify these views among some polygons.

14:16

### Video Transcript

Plans and Elevations

In this video, we will learn how to identify the plan view and the front and side elevations of a three-dimensional shape. So let’s begin by thinking about what each of these terms mean.

When we talk about plans and elevations, these are both examples of two-dimensional drawings of three-dimensional shapes. So what’s the difference? Let’s look at plans first. A plan is a two-dimensional drawing showing a three-dimensional shape when it is viewed from above, the important thing being the view from above. One way we can help remember this is to think of a building plan. A building plan might show us the view from above, for example, to see the different rooms within a building. But it wouldn’t necessarily show us what the building looks like from the front or the side. In order to see what it looks like from the front or the side, we’d need these different elevations.

An elevation is the two-dimensional drawing of a three-dimensional shape when it is viewed from the front or the side. The view from the front is called the front elevation, and the view from the side is called the side elevation. So let’s say that we have this building. It’s got a cuboid for the main part of the building and the roof is made of a pyramid. The front view would be looking at the door, and the side view would be looking at the side. If we were to consider the front elevation of this building, we’d see the front of the main building. But we’d also see the front view of the roof as well. In this case, the front of this pyramid would appear to be a triangle in two dimensions.

For the side elevation, we’d have the two-dimensional drawing from the side. And for the plan, remember, that’s when we look down from above. In this case, we’d see a rectangular shape. In general, we need the plan, the side, and the front elevation to give us an accurate view of a three-dimensional shape. Let’s say that we took our building and decided we were going to knock down half of it so that it looks like this. In this case, if we were just using the front elevation, it would still look the same as it did before. However, both the side elevation and the plan would need to change accordingly. And that’s why we need all three to give us a good idea of a three-dimensional shape.

We’ll now have a look at some questions on plans and elevations, and in the first question, we’ll need to draw the plan of a three-dimensional shape.

Which of the following is the plan of the given shape?

In this question, we can see that we’re given a cuboid or a rectangular prism with the dimensions of two centimeters, three centimeters, and four centimeters. We’re asked to find the plan of this shape. We can remember that a plan is a two-dimensional drawing of a three-dimensional shape when it is viewed from above. The view from above would mean looking downwards onto this cuboid; and therefore, the two-dimensional face at the top of the cuboid would be a rectangle. Importantly, we also know the dimensions of this rectangle. It would be three centimeters by four centimeters. Our answer would therefore be the rectangle given in option (C) of four centimeters by three centimeters.

We can eliminate the other options. If we look at option (A), it’s a square of three centimeters by three centimeters, so it’s not option (A). If we look at option (B), it’s interesting because it actually gives us the side elevation. That’s the two-dimensional drawing looking from the side view of this three-dimensional shape. But as we were asked for the plan, it’s not the answer given in option (B). We can eliminate option (D) as it’s a square of four centimeters by four centimeters. So our answer is that given in option (C).

In the next question, we’ll see how we can find the side elevation of a three-dimensional shape.

Which of the following is the side elevation of the given shape?

We can recall that an elevation is a two-dimensional drawing of a three-dimensional shape. We can say, therefore, that the side elevation is a two-dimensional drawing of a three-dimensional shape when viewed from the side. In this type of question, we’ll usually be given the direction to take as the side. It can be easy to get confused between elevations and plans, but plans are different in that they’re a two-dimensional drawing from above. In this question, however, let’s look for the side elevation. If you find visualizing this type of activity difficult, it can be useful to shade what we might see.

We might find it a little bit easier to realize that we see the sides of these four blocks on the base of the shape; however, we’d also see the side of these two blocks at the top of the shape. When it comes to adding these two blocks into our side elevation, although in the diagram we can see that they’d be set further back from the four on the base, when it comes to drawing them, we’d just draw these two blocks on top of the other four. Therefore, we’d have a rectangle two units along and three units up. Therefore, the answer is that given in option (B), and none of the other options would fit with the side elevation.

However, let’s take a quick look at option (A). This is, in fact, that the front elevation of the shape as it’s the two-dimensional drawing when viewed from the front. If we look at the two-dimensional drawing in option (C), that’s the plan view because if we looked down on this three-dimensional shape from above, we’d see a rectangle that’s four units long by two units long. But as neither of these nor options (D) or (E) give us the side elevation, then we can give our answer as option (B).

Let’s take a look at another question.

True or false: The given shape has the views shown below.

In this question, we’re given a three-dimensional shape. We’re then given a plan view, a front elevation, and a side elevation. And we need to check if these three views are true. Let’s begin by remembering the difference between plans and elevations. A plan is a two-dimensional drawing of the view of a three-dimensional shape from above. And an elevation is a two-dimensional drawing of the view from the front or the side. So the front elevation is the view from the front, and the side elevation is the view from the side. So let’s start by thinking, what would this three-dimensional shape look like from above?

If we shade the parts that we’ll see in the plan view, we’d see a shape that almost looks like it’s going to be a rectangle. We have got three units in this direction and two units in this direction. However, we’re not quite making a complete rectangle as we’re missing a section here. But what we have got here is exactly what we’re given in this plan view. Next, let’s have a look at the front elevation. That’s what we’ll see when we’re looking in this direction. So we’d see two squares sitting alongside each other along with this other square sitting on top. This is exactly what we’d see in the given front elevation, so this view is correct.

Finally, let’s have a look and see if we can work out the view from the side. From this view, we’d have three blocks sitting on the base and one on top. But is the side elevation given correct? No, it’s not. Let’s start by thinking what it would look like. Here, we’ve drawn the three blocks that sit on the base of this side elevation. This block that we’re given on top of the shape is actually sitting on top of the block on the base that’s furthest to the right. The side elevation would therefore look like this, but not the one that we’re given. We would therefore give our answer that this is false as the given shape does not have the views shown below. The plan and the front elevation are correct, but the side elevation is not.

In the next question, we’ll identify the side elevation of a prism.

Which of the following is the side elevation of the given shape?

In this question, we’re asked to find the side elevation, which means that we need to produce a two-dimensional drawing of this three-dimensional shape. We’re usually given the direction that we take as this side. Notice that if we wanted to draw the view from above, that’s called the plan view. It can be helpful to shade in what we’d see if we looked from the side. So, we’d see this rectangle at the bottom. That’s four centimeters by one centimeter. But we’d also see another part of this shape as well, this flat side of the prism.

Although when we look at this three-dimensional shape, we can see that this face would be slanted, that is, it’s not horizontal or vertical, but when we draw it, we’ll draw it as a rectangle. The height from the bottom of the shape to the top is three centimeters, so the height of the rectangle in the elevation will also be three centimeters. Our answer for the side elevation is therefore that given in option (E). But let’s have a quick look at some of the other options we were given.

Let’s look at option (A). It is, in fact, the front elevation of this shape as this is what we’d see if we looked at this three-dimensional shape from the front. As we were looking for the side elevation, however, it’s not correct for the answer. In option (B), we were given a square of four centimeters by four centimeters. This is, in fact, the plan of the given shape. It’s what we’d see if we looked at the three-dimensional shape from above. But it’s incorrect for the side elevation of the given shape. Option (C) is also incorrect. It’s a triangle. And option (D) is also incorrect. Option (D) is what we’d see if we looked at this shape from the back. We can give our answer here as option (E).

We’ll now have a look at one final question.

Which of the following is the solid shape that could have the views shown?

In this question, we’re given three different views in two dimensions of a three-dimensional shape. We’re then given five different three-dimensional shapes, and we need to work out which one of these has the elevations and plan given. Let’s begin by recalling that an elevation is a two-dimensional drawing of a three-dimensional shape from either the side or the front. The side elevation is from the side, and the front elevation is from the front. Like an elevation, a plan is also a two-dimensional drawing, but this time it’s when viewed from above the shape.

So let’s begin by looking at the side elevation. We can see that there’s three squares on the base and one square above. Let’s have a look at each of the three-dimensional shapes given in the options, and we need to be careful that we’re looking at the shape from the correct given side. We can shade the parts of the three-dimensional shape that we would see from the side. If we look at option (A), it is in fact incorrect. The side elevation of option (A) would look like this. That’d be three squares on the top and one square underneath on the left-hand side. We can eliminate option (A) because the side elevation is incorrect. If we look at option (B) from the side, we have the three squares on the base and this one square on top. Therefore, at least the side elevation of option (B) would be correct.

Let’s see if any of the other shapes would have the same side elevation. In option (C), there’d be side elevation with one square at the base and three squares along the top. It would in fact have the same side elevation as that in option (A). It is, however, incorrect as it wouldn’t fit the given side elevation. Option (D) would have two squares on the base and three squares along the top, which wouldn’t fit the side elevation. If we shade in what we would see in option (E), we can see that this would also be incorrect. It looks like we have eliminated all of the options except for option (B). So let’s check if the front elevation is also correct.

What we’re looking for in the front elevation is identical to that in the side elevation, three squares on the base and one square on the top on the left side. If we look at option (B), we’ve got three squares on the base and one square sitting on top on the left side. So the front elevation here is also correct. For the plan view then, that’s the two-dimensional shape that we would see if we looked downwards from above. Shading in the parts of the blocks that we would see from above, we can see that the plan view given would also fit with shape (B). We can therefore give our answer that the shape given in option (B) would have the views of the side elevation, front elevation, and plan that we were given.

Let’s now summarize what we’ve learned in this video. We saw that plans and elevations are two-dimensional drawings of three-dimensional shapes. A plan is the two-dimensional drawing when the three-dimensional shape is viewed from above. An elevation is the two-dimensional drawing when viewed from the front to give the front elevation or the side to give the side elevation. Finally, we should make sure that we check the diagram to find the correct directions that were given for the front and side.

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