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### Course: 6th grade (Illustrative Mathematics) > Unit 1

Lesson 9: Lesson 14: Nets and surface area# Surface area using a net: triangular prism

Here are the steps to compute the surface area of a triangular prism: 1. Find the areas of each of the three rectangular faces, using the formula for the area of a rectangle: length x width. 2. Next, find the area of the two triangular faces, using the formula for the area of a triangle: 1/2 base x height. 3. Add the areas of all five faces together, and you're done!

## Want to join the conversation?

- At1:00How did he get 1/2(30 votes)
- Like i said to selion if your talking about how he got the 1/2, thats apart of the formula. Which is, Half of the base times the height, OR, Half the height times the base(35 votes)

- i need help on nets and surface area(16 votes)
- If you don't understand this, try going back to Unit 8 - Plane figures (if you haven't already done it, complete it before going back to this). You can also try the course called "Getting ready for 6th grade."

Here is how to find areas of different parts of nets:

The formula for a triangle is 1/2 times Base times Height.

The formula for a square is Base times Height.

The formula for a parallelogram is to break it into two smaller triangles, switch it around to make a square, and find Base times Height of the square.

The formula for any other shape is break into other shapes (triangles, squares, etc.), find the area for all the broken-up shapes, and add it all up.

Once you have found the area for all the parts of the net, add the parts together to find the area of a net.

Hope this helps!(12 votes)

- How many nets for a prism is there?(14 votes)
- There are 9 nets(2 votes)

- sooo i ahve a question to anyone who whould like too answer me....... HOW DO YOU DO THIS? im so lost its sad can yall please help!(7 votes)
- A= HB/2 (Half of the base times height, Thats the formula for a triangle, i dont have time to give you the other formulas but i hoped this helped.(12 votes)

- Do you always have to multiply by 1/2?(7 votes)
- If you're trying to find the surface area of the triangles, then yes. You always have to multiply by 1/2 to find the area of the triangles.(5 votes)

- is there a better way to explain this like a talk through b/c is still dont understand.(10 votes)
- how do you know if you're placing the numbers correctly??(10 votes)
- I'm so confused we do this in school and this is how my teacher does it but when id do my go formative it red i did the steps with "Sal" and its red when it supposed to be green i'm just so lost this is why somethings I hate math(6 votes)
- this video make me have more questions...(5 votes)

## Video transcript

- [Instructor] What I
want to do in this video is get some practice finding
surface areas of figures by opening them up into
what's called nets, and one way to think about
it is if you had a figure like this, and if it was
made out of cardboard and if you were to cut it,
if you were to cut it right where I'm drawing this red,
and also right over here and right over there and right over there and also in the back where
you can't see it just now, it would open up into something like this. So if you were to open it up, it would open up into something like this, and when you open it up, it's much easier to figure out the surface area. So the surface area of this figure, when we open it up, we can just
figure out the surface area of each of these regions. So let's think about it. So, what's, first of
all, the surface area? What's the surface area
of this right over here? Well, in the net that
corresponds to this area. It's a triangle. It has a base of 12 and a height of eight. So this area right over
here is going to be 1/2 times the base, so times 12,
times the height, times eight. So this is the same thing as
six times eight, which is equal to 48 whatever units, square units. This is gonna be units of area. So that's gonna be 48 square units. And up here is the exact same thing. That's the exact same thing. You can't see it in this figure. If it was transparent,
if it was transparent, it would be this back
side right over here. But that's also going to
be 48, 48 square units. Now we can think about the areas of, I guess you could consider
them to be the side panels. So that's a side panel right over there. It's 14 high and 10 wide. This is the other side panel. It's also, this length right over here is the same as this length, so it's also 14 high and 10 wide. So this side panel is
this one right over here. And then you have one on the other side. And so the area of each
of these, 14 times 10, they are 140 square units. This one is also 140 square units. And then finally we just have
to figure out the area of, I guess you could say
the base of this figure. So this whole region right
over here, which is this area, which is that area right over there. And that's going to be 12 by 14. So this area is 12 times 14,
which is equal to, let's see, 12 times 12 is 144, plus
another 24, so it's 168. So the total area is
going to be, let's see, if you add this one and
that one, you get 96, 96 square units. The two magenta, I guess you could say, side panels, 140 plus 140, that's 280. 280. And then you have this
base that comes in at 168. Want me do that same color? 168, 168. Add them all together and
we get the surface area for the entire figure, and it was super valuable
to open it up into the net 'cause we could make sure
we got all of the sides. We didn't have to kind of
rotate it in our brains, although you could do that as well. So six plus zero plus eight is 14. Regroup the one 10 to the tens place. So it's now one 10. So one plus nine is 10, plus eight is 18, plus six is 24. And then you have, oops. And then you have two
plus two plus one is five. So the surface area of this figure is 544, 544 square units.