00:02
Okay, we've got a trapezoid.
00:04
I tried to make it as generic as i could, because we don't know anything about it.
00:13
Well, we know some things about it, but we don't know its exact shape.
00:18
We know that it has an area of 3440, and we know that the ratio of the parallel sides, the bases, is 3 to 5.
00:34
So i could call this small base 3x, and this larger base 5x, and then they'd have a ratio of 3 to 5.
00:48
Then we're going to draw one of the diagonals, and that will divide it into two triangles.
00:58
And we want to know the area of those triangles.
01:03
So one thing i notice about those two triangles is that they actually have the same height.
01:11
So here would be the height of the triangle with 5x as the base, and here would be the height of the triangle with 3x as the base.
01:32
And that's the same height as the height of the trapezoid.
01:39
And even if we had drawn the other diagonal, it still would have worked out the same.
01:46
So let's go ahead and write formulas for the area of the two triangles.
01:55
So the top triangle, let's say that's area 1.
02:00
Well, that's going to be 1 half base times height.
02:10
So what's 1 half times 3? let's call that 1 .5xh.
02:17
I'm running out of room.
02:22
1 .5xh, and let me just erase that right there.
02:30
Okay, and then area 2, the bottom triangle.
02:38
So area 1, area 2, that's going to be 1 half base times height.
02:44
So the base is 5x, and the height is h...