Finding perimeter of shape with semicircles

0:00- [Instructor] We are told two smaller semicircles of radius five centimeters each are joined by two larger semicircles of radius, 10 centimeters each. This is a cool looking design. This is a semicircle of five centimeters radius and then a semicircle of 10 centimeters and then a semicircle of five centimeters and then a semicircle of 10 centimeters.

0:19Find the exact perimeter of the shape. So pause this video, have a go at this before we do it together. Alright, so we really just wanna figure out all of the lengths of everything that we see drawn here. And one simplification is if we wanna find this length right over here, we could add this to this because these two semicircles combined form a whole circle.

0:43So they form a whole circle with a radius of 10 centimeters. And then we could do that for the two smaller semicircles as well. If we take this semicircle with radius five centimeters and add it to this semicircle of radius five centimeters, well then we just get a whole circle of radius of five centimeters.

1:06So really if we just find the perimeter of this and add it to the perimeter of this, then we have the perimeter of this entire shape, this weird looking wavy looking thing. So what's the perimeter here? We know, or I should say the circumference 'cause if the perimeter of the circle we say is circumference.

1:22So circumference is equal to, circumference is equal to two times pi times the radius. Well in this case it's going to be two times pi times 10, which is equal to 20 pi centimeters. And in this situation right over here, it's going to be equal to 2 times pi times 5 which is equal to 10 pi centimeters.

1:45And so if we were to add these two things together, 20 pi centimeters plus 10 pi centimeters to get the total of everything here, we get 30 pi centimeters and we're done.