Perimeter of semicircles and quarter circles

A semicircle has a radius of 10 cm. Find the perimeter of the semicircle. Here's the semicircle. Half a circle, and its radius is 10 centimetres. Take pi as three point one four. Perimeter means the whole way round. So let's go round it. Round the curve. And back along the bottom. Two pieces. The curve, and the straight edge. That straight edge wasn't there before we cut. Here's the whole circle, and here's the cut that made this half. Cutting a circle makes new edges, and they count. The curve first. This curve has a name. It's called the arc. The arc is half of the circle's whole edge. A whole edge, rolled out, is pi times the diameter. So this curve is half of that. So we can write the rule down. The arc is a half, times pi, times the diameter. The radius is 10, so the diameter is 20. Half, times three point one four, times 20. Cross out the 2 and the 20 leaves 10. That's thirty one point four centimetres. Now the whole way round. The perimeter of a semicircle is the arc, plus the diameter. That's the straight edge. So that's the arc, thirty one point four, and the straight edge, 20. Fifty one point four centimetres. Sometimes a question gives you no value for pi at all. It says leave your answer in terms of pi. Then you just stop earlier. Half of 20 is 10, so the curve is 10 pi. And the whole way round is 10 pi plus 20. The number never gets worked out, and that's allowed.

Your turn. A quarter circle has a radius of 14 cm. Find the perimeter of the quarter circle. Take pi as 22 over 7. Let's go round it first. Try it first. Pause if you like. Round the curve. Down one straight edge. And along the other. Two straight edges this time, not one. A quarter has two cuts. Same rule. The arc is a quarter, times pi, times the diameter. The radius is 14, so the diameter is 28. A quarter, times 22 over 7, times 28. Cross out the 4 and the 28 leaves 7. Then cross out the two 7s. 7 divided by 7 is 1. That leaves 22 centimetres. Then the whole way round. 22, and 14, and 14 gives 50 centimetres. Perimeter is the whole way round. The arc is part of it. The straight edges are part of it too. They come from cutting. A semicircle has 1 straight edge. A quarter circle has 2. Add the arc and the straight edges. That is the perimeter.