Which has greater area? A parallelogram with base length 10cm and perpendicular height 6cm, or a circle of diameter 8cm.

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The question requires you to work out the area of the two shapes individually and then compare your answers to see which is greater.

Firstly, to calculate the area of the parallelogram you must recall the formula 'area = base x perpendicular height'. The perpendicular height is the maximum length of a line drawn at a right angle (90 degrees) from the base. This formula makes sense because you can imagine cutting off one 'overhanging' end of the parallelogram and attaching it to the other side to form a rectangle. This is why the formula is similar to the area of a rectangle (base x height).

Using this formula the area of the parallelogram = 10 x 6 = 60cm2.

For the area of a circle, you need to remember the formula ' area = pi x radius'. There are many ways of remembering this very important formula including rhymes and songs. Pi is a fixed number and can be found on a calculator so there is no need to work this out. However to get the radius of the circle, you need to remember that radius = diameter divided by 2. This is because the diameter is the distance from one side of the circle to the other opposite side, while radius is the distance from the centre to the edge.

Using this, we can work out the radius of the circle = 8 / 2 = 4. Putting this into the formula for area we get, area of circle = pi x 4= pi x 16 = 50.27cm2 (to two decimal places).

We can now see that the area of the parallelogram (60cm2) is greater than the area of the circle (50.27cm2) so the answer is the parallelogram.

Sam W. GCSE Maths tutor

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