Finding the volume of a prism with a polygon base on a grid
About this video
The video finds the volume of a hexagonal prism with height 5 units whose base is drawn on a grid. The hexagon is split into four triangles of 4 square units each and a 5 by 8 rectangle, giving a base area of 56 square units, so the volume is 56 × 5 = 280 cubic units.
You'll be able to
- find the area of a polygon by breaking it into triangles and rectangles.
- find the volume of a prism by multiplying the base area by the height.
Key words
- hexagonal prism
- A prism whose two matching bases are hexagons (six-sided shapes).
- area of a triangle
- One half times base times height.
- cubic units
- The units used for volume, counting how many unit cubes fit inside.
Transcript
- [Instructor] The base of a hexagonal prism is shown on the grid. Each square on the grid represents one square unit. The height of the prism is five units. What is the volume of the hexagonal prism? Pause the video, have a go at that. All right, so let's just visualize what's happening.
We have a prism where the base is this hexagon, so the base might look like that and then it has a height of five units. So do my best to draw that, and then the top of it will look the same as the base. So what we need to do to figure out the volume of this...
I hope this was kind of making sense. It's a little bit messier of a drawing than I wanted. Is, for a prism like this, if you can figure out the area of the base, maybe I'll shade that in in pink and then you multiply that times the height, which is five units, so you multiply it times the height of five units, then you're going to get its volume.
So let's figure out the area of the base and we'll just multiply that by five. And to figure out this area, they gave us a nice grid, and we can actually break this hexagon up into pieces here and figure out the area of each of these pieces and then that will help, so let's do it this way.
So the area of a triangle is one half base times height. One half base times height. So this triangle right over here, its base is two, its height is four. Two times four is eight, but you take half of that. It's four square units. By that same logic, this one would also be four, this one would be four, this one would be four.
And then this big rectangle right over here, it's one, two, three, four, five by one, two, three, four, five, six, seven, eight. Five times eight, five times eight is equal to 40. And so if we add all of this up, we have four fours. That's 16 plus 40. The entire base right over here is going to be 56 square units, 40 plus 16.
Now we just multiply that times five. 56 times five times the height of the prism, and that's going to get us to... Let's see, six times five is 30. Five times five is... Or 50 times five is 250. 250 plus 30 is 280 cubic, cubic units, and we are done.
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