ACARA v9 CONTENT DESCRIPTION “solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units”
Builds on choosing metric units, and on the multiplication met in number. Year 5 applies measurement to two key quantities: perimeter, the distance around the edge of a shape, and area, the amount of surface it covers. For regular shapes like rectangles these can be found with simple rules, while for irregular shapes they are built up by adding lengths or combining smaller pieces. Working in suitable metric units, and solving practical problems with them, turns measuring into a tool for real situations, from fencing a garden to tiling a floor.
Perimeter is the distance around
Perimeter is the total distance around the outside of a shape. Walking right around the edge and adding the length of every side gives the perimeter, so a shape with sides of six, four, six and four centimetres has a perimeter of twenty centimetres. Because perimeter is a length, it is measured in length units such as centimetres or metres. Perimeter answers practical questions about going around something: the fencing for a paddock, the edging for a garden bed, or the ribbon around a parcel all depend on the perimeter rather than the space inside.
Perimeter is the distance around
Add the length of every side.
Perimeter is the distance all the way around.
Area is the space inside
Area is the amount of surface a shape covers, the space inside its edges. Area is measured in square units, such as square centimetres or square metres, because it counts how many unit squares fit inside the shape. A rectangle six squares wide and four squares tall holds twenty-four unit squares, so its area is twenty-four square centimetres. Area answers questions about covering a surface: the paint for a wall, the turf for a lawn, or the tiles for a floor all depend on area. Perimeter and area measure different things, and confusing them leads to the wrong answer.
Area is the space inside
Count the unit squares, or multiply the sides.
Area counts the unit squares that fit inside.
Perimeter and area of a rectangle
Rectangles are regular enough to have simple rules. The perimeter is found by adding the four sides, which is the same as adding the length and width and doubling, while the area is found by multiplying the length by the width. A rectangle five centimetres long and four centimetres wide has a perimeter of eighteen centimetres and an area of twenty square centimetres. A square is a special rectangle with equal sides, so its perimeter is four times one side and its area is one side multiplied by itself. These rules make regular shapes quick to measure.
Perimeter and area of a rectangle
Area multiplies the sides; perimeter adds them.
Choose area or perimeter and calculate.
The perimeter of irregular shapes
Irregular shapes have no single formula, but their perimeter is found the same way as any other: by adding the lengths of all the sides. An L-shaped room, for instance, has six sides, and adding them all gives the distance around it. The key is to account for every edge, including the ones that turn inward, and to use the same unit throughout. Because perimeter is always just the total of the sides, it works for any shape at all, however many corners it has, as long as each side length is known.
The perimeter of irregular shapes
Add every side, including the inward ones.
For any shape, the perimeter is the sum of all its sides.
The area of irregular shapes
The area of an irregular shape is found by breaking it into simpler pieces, usually rectangles, and adding their areas. The same L-shape can be split into two rectangles: a larger one and a smaller one. Finding the area of each rectangle and adding them gives the total area of the L. Choosing where to split, so that each piece is a rectangle whose area is easy to calculate, is the main skill. Counting unit squares works too, but splitting into rectangles is faster and works even when a shape is large.
The area of irregular shapes
Break it into rectangles and add the areas.
Split an irregular shape into rectangles, then add their areas.
Choosing the right measure and unit
Solving practical problems means choosing the right measure and the right unit. Decide whether the question is about going around a shape, which needs perimeter, or about covering it, which needs area; then pick a sensible metric unit, length units for perimeter and square units for area. Add the sides for perimeter, and multiply or split into rectangles for area. With these habits a child can measure regular and irregular shapes, work in suitable units, and solve the everyday problems of fencing, covering and building that perimeter and area describe.
Quick self-check
1. The perimeter of a shape is...
2. The area of a shape is...
3. A rectangle is 6 cm long and 4 cm wide. Its area is...
4. The perimeter of that 6 cm by 4 cm rectangle is...
5. A good unit for the area of a classroom floor is...