Finding a circle's radius or diameter from a composite figure

A circle fits exactly inside a square. Here's the square. And here's the circle, fitting exactly inside it. The perimeter of the square is 56 centimetres. Find the area of the circle. Take pi as 22 over 7. Try it first. Pause if you like. The area of a circle is pi, times the radius, times the radius. That's the first line, every time. Now look at the circle. There's no radius on it. There's no number on it at all. So where does the radius come from? Read that first sentence again. It fits exactly inside a square. So the circle is exactly as wide as the square. Right across the circle is one side of the square. So now the question is, how long is one side of the square? Look, the perimeter of a square is the whole way round. One side, two sides, three sides, four. So 56 centimetres is made up of all 4 equal sides of the square. So the length of one side is 56 divided by 4. That's 14 centimetres. And the circle is as wide as that. So 14 goes right across the circle. The radius is half of it. 14 divided by 2. The radius is 7 centimetres. Now the rule has what it needs. 22 over 7, times 7, times 7. That's one hundred and fifty four. The area of the circle is one hundred and fifty four square centimetres. If you took the 56 straight to the circle, here's what happened. Always remember, the 56 centimetres is the whole way round the square. So here's what to remember. The perimeter of a square is 4 equal sides, so one side is 56 divided by 4. The circle fits exactly inside, so one side of the square is what goes right across the circle. And half of that is the radius. When a question says one shape fits exactly inside another, it is telling you a length.