Calculate the area of a circle where the circumference of the circle and sides of the square are tangential at 4 points.

Note this is:AQA GCSE Mathematics (8300) June 2017Paper 1: Non-Calculator 8300/1H - HigherQuestion 12The area of a square is its base multiplied by its height. In our case this gives an area containing multiple squares of 1 cm by 1 cm. Therefore, given the area, we may find the two numbers (the base and height) that multiply together to produce it. The next bit will depend on the students knowledge of times-tables. This is where I'd suggest ruling out obvious numbers; 10 x 10 is 100, so its less than 10, 5 x 5 is 25, 6 x 6 is 36, so it's larger than these. Eventually finding 8 x 8, where the student may conduct arithmetic to find 64. Looking at the picture, we can see that both shapes have a similar centre point, and hence any line from there to where the circle and square are touching has equal distance. A line all the way through represents both the circles diameter and the length of the side of the square. The diameter is therefore 8 cm. We know that the radius is half of the diameter, which is then 4 cm. Then we know that the area of a circle is the product of Pi and the radius squared. 4 x 4 is 16, multiplied by Pi is 16 Pi (answer is given in terms of Pi). Descriptions and pictures of the derivation of circumference and area for a circle may be given if questioned by the student, or if they show any sign of interest or confusion on their use - also depending on the time left and the rest of the lesson material.