Perimeter, Area, Volume

Perimeter of complex shapes

Area of a rectangle

Area of composite shapes

Area of triangles

Volume of cubes and cuboids

Prerequisite Knowledge

• measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
• calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm²) and square metres (m²) and estimate the area of irregular shapes
• estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]
• recognise that shapes with the same areas can have different perimeters and vice versa
• recognise when it is possible to use formulae for area and volume of shapes

Key Concepts

• The perimeter of a shape is the distance around the outside.  It is measured in units such as centimetres, millimetres, inches, feet, and metres.
• The area of a shape is a measure of how much space there is on the surface.  Area is measured in square units, written for example as cm².
• To find the area of a composite shape it is easier to split the shapes into distinct rectangles and find the sum of each area.
• The area of a triangle can be found as half the area of a rectangle.
• The volume of a shape is the space contained inside it.  Volume is measured in cube units, written for example as cm³.

Working mathematically

Develop fluency

• Use language and properties precisely to analyse 2-D and 3-D shapes

Reason mathematically

• Begin to reason deductively in geometry,

Solve problems

• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

Shape

• Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms
• Calculate and solve problems involving: perimeters of 2-D shapes and composite shapes.