Perimeter, Area, and Volume

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infoWhy this? Measurement of compound shapes, circles, and solids develops spatial reasoning and disciplined use of formulae and units. Circumference, area, and volume also distinguish linear, square, and cubic measures in meaningful contexts.

scheduleWhy now? This unit extends Year 7 work on polygon perimeter and area to trapezia, circles, compound boundaries, and three-dimensional volume. It establishes the formula fluency needed for prisms, cylinders, surface area, and composite shapes.

The perimeter of a shape is the total distance all the way around its outside edge.
To find the perimeter of a compound shape, only the lengths on the outer boundary are added, and any missing side lengths must be worked out first from the given measurements.
Area measures the amount of surface inside a 2D shape and is written in square units such as `cm^2` or `m^2`.
A trapezium is a quadrilateral with one pair of parallel sides.
The area of a trapezium is given by `\frac{1}{2} \times (a+b) \times h`, where `a` and `b` are the parallel sides and `h` is the perpendicular height.
In a trapezium, the height is the shortest distance between the parallel sides and must be perpendicular to them.
A circle is the 2D region enclosed by its circumference, and the circumference is the boundary whose points are all the same distance from the centre.
The radius of a circle is the distance from the centre to the circumference, and the diameter is twice the radius.
The circumference of a circle is the distance around the circle and can be calculated using `\pi d` or `2\pi r`.
The area of a circle is calculated using `\pi r^2`, which means `\pi` multiplied by the square of the radius.
The symbol `\pi` represents the constant ratio of a circle’s circumference to its diameter and is approximately `3.14`.
Volume measures the amount of space inside a 3D shape and is written in cubic units such as `cm^3` or `m^3`.
The volume of a solid can be found by counting how many unit cubes exactly fill it with no gaps or overlaps.
The volume of a cuboid is calculated using `\text{length} \times \text{width} \times \text{height}`.
A cube is a special cuboid with all edges equal, so its volume can be calculated using `s^3`.
Perimeter uses linear units, area uses square units, and volume uses cubic units.

rocket_launchYou must be able to

Find the perimeter of a compound shape by identifying any missing side lengths from the given dimensions and then adding all the outer edges only.
Calculate the area of a trapezium by selecting the two parallel sides, using the perpendicular height, and substituting into `\frac{1}{2} \times (a+b) \times h`.
Identify the radius or diameter of a circle from a diagram or measurement and convert between them using the fact that the diameter is twice the radius.
Calculate the circumference of a circle by choosing either `\pi d` or `2\pi r`, substituting the correct value, and giving the answer in the correct linear units.
Calculate the area of a circle by squaring the radius first and then applying `\pi r^2`, giving the answer in the correct square units.
Determine the volume of a solid made from unit cubes by counting cubes systematically in rows, columns, or layers, including cubes that may not be visible from one view.
Calculate the volume of a cube or cuboid by multiplying its three dimensions and expressing the result in the correct cubic units.
Check whether an answer should be written in units, square units, or cubic units by deciding whether the problem is about perimeter, area, or volume.

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