While this might seem a simple prompt, it can lead to a number of intriguing questions for students in lower secondary school.
An issue that regularly arises is the degree of accuracy appropriate for the area of the circle in comparison to the areas of the rectangle and triangle. If the areas of the rectangle and triangle are 20cm2, for example, is the statement proved correct if the area of the circle is within one tenth of a square centimetre? ... or one half? Can the areas ever be exactly the same? Students might be able to use inverse operations to deduce that the radius of the circle is, in our example, √(20/π). Is it acceptable to leave the solution in terms of π?
- How do you work out the area of an obtuse-angled triangle?
- How do you work out the area of a circle?
- Can the radius of the circle be a whole number if its area is a whole number?
- Can the dimensions of the three shapes all be whole numbers or must there be decimals?