00:04
All right, so we're given this strange looking shape.
00:06
We're told that it's made out of squares and either semicircles or quarter of circles.
00:12
And we're asked to find the area and the perimeter of the shaded region, what i haven't read there.
00:17
All right, so what i'm going to do is just take one of those things out for a second here, just to kind of show, make sure we see what we're looking at.
00:25
That wasn't a very good one there.
00:26
Let me try that again, just to make it a little bit more feasible there.
00:30
Okay, so basically this would be one of the one of the one.
00:32
Quarter of a circle.
00:35
All right.
00:36
And we know that this is eight centimeters, which is the radius, right, because this would be the center of the circle.
00:42
All right.
00:43
So the circle, the whole circle, would be pi times the radius squared.
00:48
So the whole circle would be 64 pi, eight times eight is 64, so 64 pi.
00:54
But we only have a quarter of it, and 64 divided by 4 is 16.
00:57
So this whole region would be 16 pi.
01:01
Now, what i'm going to do, because i don't want all of that stuff, is i'm going to slice it down the center here and just find this piece.
01:12
All right, and in order to do that, i have to subtract out this triangle.
01:17
While this triangle is one half of eight times eight, since this is a square, i know this side is also eight.
01:24
Eight times eight would be 64, and then half of that is 32.
01:30
So the red shaded area is 16 pi minus 32 for the area.
01:38
All right.
01:39
But if you go back, you know, that is half of what we actually wanted, right? that would be this part up here, but i know it's going to be the same on the other side...