Total and lateral surface area using a net rectangular pyramid
About this video
Using a net, the video finds the surface area of a rectangular pyramid with a 7 m by 3 m base. Two triangles have base 7 and height 5.1, and two have base 3 and height 6, giving a lateral surface area of 35.7 + 18 = 53.7 m^2. Adding the 21 m^2 base gives a total surface area of 74.7 m^2.
You'll be able to
- draw or picture the net of a rectangular pyramid.
- find the lateral surface area by adding the areas of the triangular faces.
- find total surface area by adding the base to the lateral area.
Key words
- net
- A flat shape that folds up to make a 3D solid.
- lateral surface area
- The total area of the side faces, not including the base.
- total surface area
- The area of all the faces, including the base.
- altitude
- The height of a triangle, measured at a right angle to its base.
Transcript
- [Instructor] So I'm going to do a similar net here. Let me start with our base, just to visualize it. So this base here is, and sorry for my shaky hand, it's 7 meters wide and it is 3 meters deep. And now let me take this front side and take it out like that.
And it looks like the backside is symmetric to that. So if we take this front side, actually let me do this in a different color so that we can track things. Maybe I'll draw these lines right over here in this purple color. So if we were to do that, we were to open it up like this.
We know from here to there is 5.1 meters. So this distance right over here, this altitude right over here, is 5.1. And we have the same thing going on on the other side, where this distance right over here, I could have drawn this way neater, is 5.1. And then we can open up the two sides.
So let me do that in a color that you can actually see. So this side right over here, if we were to open it up like that, we know that this height right over here, which is the same thing as this, the length of that altitude, that is 6 meters. And then it's symmetric on the other side.
So this is going to be 6 meters. So if we go to figuring out the lateral surface area, it's going to be these two purple triangles. Each of them are going to be 7 times 5.1 times one half but we have two of them. So I could say, 7 times 5.5 divided by 2, that's this one.
And then we have this one, which is gonna be the same, 7 or not 5.5, I almost made a mistake. 7 times 5.1 divided by 2 plus 7 times 5.1 divided by 2. Well this, when you add these two together, you're just going to have 7 times 5.1 is going to be this one, plus this one, 'cause they're each half of that.
And then to that, you're going to add the area of this blue one right over here, is gonna be 6 times this length, 6 times 3 times one half. So it's six times three divided by two or times one half. And then this one as well is gonna be six times three times one half or divided by two.
Or if you add these two together, that's just the same thing as six times three. That's the same thing as six times three. And so seven times 5.1, seven times five is 35, seven times is 0.1 is 0.7. So this is 35.7 plus 18 and let's see, if I were to add 20, that would get me to 55.7.
So it's gonna be two less than that. So this is going to be 53.7. And I think the units here, yes, the units here are in meters, square meters for lateral surface area. If we want the total surface area, we then want to add in the area of this base, of this base right over here.
And that is going to be three times seven or 21 square meters. So it's gonna be 21 square meters, the base, plus the lateral surface area, 53.7 square meters, which is going to be equal to 74.7 square meters. And we're done.
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