Measurement

Lesson

As we saw in our two earlier chapters of perimeter (here and here), finding the perimeter of simple 2D shapes or polygons is simply a matter of adding up the lengths of the sides. Well, now that we also know how to find the perimeter of a circle (called the circumference), we can find the perimeter of composite shapes that involve full circles, or semi circles. The concept is the same, that all perimeters can be found by adding up one side at a time as we travel around the shape (even if the side is circular).

This is a composite shape, made up of a semicircle and a rectangle. Although, we are missing one side of the rectangle and the base of the semicircle as that common line lies inside the shape.

We have the following:

- $3$3 straight sides : $2$2 of length $4$4 and $1$1 of length $8.4$8.4.

The sum of these lengths = $2\times4+8.4$2×4+8.4 = $16.4$16.4cm

- A semicircle of radius $\frac{8.4}{2}=4.2$8.42=4.2cm.

This length = $\frac{2\pi\times4.2}{2}$2π×4.22 = $4.2\pi$4.2πcm.

In total we could write the perimeter as

$2\times4+8.4+\frac{2\pi\times4.2}{2}$2×4+8.4+2π×4.22 | $=$= | $16.4+4.2\pi$16.4+4.2π cm |

$=$= | $29.6$29.6 cm (to $1$1 decimal place) |

Of course because perimeter is a measure of length, we need to make sure we use any units we are given. Remember from our chapter on units of length, that common units for lengths are millimetres (mm), centimetres (cm), metres (m) and kilometres (km).

All of these could be used to measure the perimeter of different sized objects. Millimetres could be used to measure the perimeter of a sim card, centimetres to measure the perimeter of a wallet, metres to measure the perimeter of a room and kilometres to measure the perimeter of a town.

It is also good mathematical practice to use the word 'units', if no particular unit for the context or question is given.

Another good practice is to perform all calculations that involve $\pi$π at the end - this reduces errors compounding throughout the calculation.

Find the circumference of the circle shown, correct to two decimal places.

Find the perimeter of the shape (shaded) shown.

Give your answer correct to $2$2 decimal places.

Find the length of wire needed to create the frame of this rectangular prism.

Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders