Finding the area of a tilted square
About this video
The video finds the area of a square drawn tilted on a grid by splitting it into four right triangles and a small square in the middle. Each triangle has base 4 and height 7, so area 14, and the middle square is 3 by 3, so the total area is 4 x 14 + 9 = 65 square units.
You'll be able to
- find the area of a tilted square by breaking it into triangles and a smaller square.
- use area of a triangle = 1/2 x base x height.
- add the areas of the parts to find the area of the whole shape.
Key words
- area
- The amount of flat space a shape covers, measured in square units.
- square units
- The unit for area: how many 1-by-1 squares would fit inside a shape.
- base and height
- For a triangle, the base is one side and the height is the straight distance at a right angle from that side to the opposite corner.
Transcript
- [Instructor] So we're asked, what is the area of this square? Pause this video and see if you can figure it out. All right, so there's many ways that we can approach it, but one way to approach it is actually to try to break up the square into things that we know the dimensions of.
So maybe a whole series of triangles might do the trick. Let me see what we can do here. So I like to do my problems in real-time with you, so I haven't solved this before either. I can figure out the area of that triangle. I could figure out the area of this triangle.
I think I see what I'm doing here. I can figure out the area of this triangle, and I can figure out the area of that triangle. And then I can also figure out the area of this inner square here. So yes, let's do that. So each of these triangles have a base of four units and a height of one, two, three, four, five, six, seven units.
So this is going to be one-half times four times seven, because the area of a triangle is one-half base times height. Four times seven, 28, times one-half is equal to 14 square units. Now, all of these triangles, they're all oriented differently, but they're all, this one is seven by four.
So same thing, it has an area of 14 square units. This one has an area of 14 square units. This one has an area of 14 square units. And the center one, you can count out the squares or you can see it's three by three. So this has an area of nine square units. So the area of this total first original square is going to be 14 plus 14 is 28.
We have another 28 right over here. So 28 plus 28 plus nine, 28 plus 28 plus nine. This is 56 plus nine, which is equal to 65 square units. I could write it like this, units, units squared. Did I, I'm most worried whether I added correctly. Yes. 56 plus nine is 65 and we're done.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.