The questions have been carefully designed to increase in difficulty level as you progress. The questions start with basic areas of circles. As your confidence develops, you can tackle some of the more challenging questions.

The harder questions include compound areas and there are also some areas of other polygons to consider too e.g. areas of rectangles and triangles.

All questions have been designed in high resolution with stunning colours.

# Areas of Circles Worksheets

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## My process for deriving the area of a circle with students

I always start by getting students to measure the circumferences and diameters of various tins of food (or any circular objects).

Place the measured values in a table of results with headings of CIRCUMFERENCE, DIAMETER, and a third column heading for CIRCUMFERENCE \(\div\) DIAMETER.

Students can use calculators to calculate the third column. What they should notice is that values are very close to pi. In fact, what they should notice is that larger-diameter objects will give a value closer to pi.

Label a circle with the diameter and circumference.

Draw a rectangle on the board and ask students to tell you the formula for the area of a rectangle.

Now start to divide the circle into small sectors and place them into the rectangle.

Ask students to connect the diameter and circumference to the rectangle i.e. the radius is the width of the rectangle and half of the circumference becomes the length of the rectangle.

From here, students may be able to derive the formula for the area of a circle by considering the area of the rectangle.

## Tips for teaching the area of a circle

Show students where the formula comes from e.g. use the process listed above.

Review the keywords associated with area and circles e.g. radius, circumference, diameter, pi, etc.

Go through the use of calculators to ensure students are familiar with the correct input of values, especially when it comes to using pi and powers.

I tend to avoid using powers if students are prone to making errors with orders of operations or with the operation of their calculators i.e. I will use:

\begin{align}

A &= \pi r^2\\\\

A &= \pi\times 5^2\\\\

A &= 3.142 \times 5 \times 5\\\\

A &= 78.55 cm^2

\end{align}

Encourage students to use manipulatives such as circles made from paper. If you have access to a laser cutter in school then produce a variety of circles for students to measure. Using thick acrylic or MDF allows the students to also measure the circumference.

Use real-world examples. There are usually plenty of examples around a school. An example may include calculating the cost to tile/carpet a circular shape.

## Some example projects involving areas and circumferences of circles

Have students create a game or activity that involves calculating the area of circles. This could be a board game, card game, or online interactive game.

Have students design a circular outdoor playground and calculate the area of the playground using the formula for the area of a circle. They can use this information to determine how many play structures they can fit in the playground.

Students could explore the relationship between perimeter (circumference) and area. They could investigate different shapes and should realise that a circle will maximise the area for the smallest perimeter.

Have students design a circular garden bed and calculate the area of the bed using the formula for the area of a circle. They can use this information to determine how many plants they can fit in the bed based on the required area needed for each plant. They could then calculate the 'wasted' space.