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Perimeter and area - WJECCircles

Knowing how to find the perimeter or area of a shape can be useful in everyday life - from wrapping a present to buying a carpet. Use it in calculations to find the amount of materials needed or cost.

Part of Maths Numeracy (WJEC)Geometry and Measure

Circles

When working with circles it is important to know the following definitions:

The radius (r) of a circle is the distance from the centre to the outside of the circle.

A circle with a line from the centre to the outside labelled 鈥榬adius鈥

The diameter (d) of the circle goes from one side of the circle to the other, through the centre.

A circle with a line going from one side to the other passing through the centre labelled 鈥榙iameter鈥

If you are given one, you are able to calculate the other and may need to for certain calculations:

radius = diameter 梅 2

diameter = radius 脳 2

The perimeter of a circle is called the circumference.

\(\text {circumference = ~\pi~\times~diameter}\)

or

\(\text {circumference = 2 \times~\pi~\times~radius}\)

\(\pi\) is approximately equal to 3.14.

We will use the \(\pi\) function on the calculator in these calculations.

Question

Calculate the circumference of the slice of orange when the radius is 6 cm.

A slice of orange with a radius equal to 6 cm

Question

The circumference of a wheel is 200 cm. Calculate the diameter to the nearest centimetre.

A wheel with a circumference of 200 cm

\(\text {Area of a circle =}~\pi~\times~\text {r}^{2}\)

Remember that \(\text {r}^{2}~\text {= r \times~r}\)

If you are given the diameter, you must remember to halve it so you are using the radius.

Question

Find the area of the surface of a 10p coin when the radius is 12.25 mm. Give your answer to two decimal places.

A 10 pence coin with a radius of 12.25 mm

Given the area of a clock is 1,250 cm2, calculate its diameter to the nearest centimetre.

A clock face with area equal to 1,250 cm squared

Rearrange the formula for area:

A = \(\pi \times {r}\)2

\({r}\)2 = A 梅 \(\pi\)

\({r}\)2 = 1,250 梅 \(\pi\) = 397.8873577

\({r} = \sqrt{397.8873577}\)

\({r}\) = 19.94711402

\({d}\) = 2 x \({r}\) = 2 x 19.94711402 = 39.89422804

diameter = 40 cm (to the nearest cm)

Calculate the area and perimeter of the semi-circle stained glass window.

A semi-circular stained glass window with diameter equal to 1 m

Diameter of circle = 1 m

Radius of circle = 0.5 m

\(\text {Area of whole circle =}~\pi~\times \text{r}^{2}\)

\(\pi\) 脳 0.52 = 0.7853981634

Area of semi-circle = 0.7853981634 梅 2 = 0.3926990817 m2 = 0.39 m2 (to two decimal places)

\(\text {Circumference of whole circle =}~\pi~\times \text {d}\)

\(\pi\) 脳 1 = 3.141592654

Circumference of half circle = 3.141592654 梅 2 = 1.570796327 m = 1.57 m (to two decimal places).

Add on the diameter for the perimeter of the semi-circle:

Perimeter = 1.57 + 1 = 2.57 m (to two decimal places).

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Further examples for Higher tier
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Area of composite shapes

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