polyhedron with base and identical parallel opposite side with corresponding edges joined by parallelograms.

Faces are the flat 2D surfaces of a 3D shape.

The net of a 3D object is a 2D representation of its faces that can be folded up into the 3D object.

The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.

Surface area of prisms

Maths

Checking understanding of perimeter

Checking understanding of area

Multiplicative relationships in circles

Circumference of a circle

Area of a circle

Using the formula for the area of a circle

Area of composite shapes

Perimeter of composite shapes

Finding a length in composite shapes

Surface area of cuboids

Properties of prisms

Surface area of cylinders

Volume of prisms

Volume of cylinders

Problem solving with perimeter, area and volume

In this unit, pupils have derived the formula for the circumference and area of a circle. In the future unit, this knowledge is combined with knowledge of fractions to find the arc length and area of a sector.

 In the prior unit, pupils learnt how to derive and use the formula for the area of a triangle and trapezium. In this unit, this knowledge is called upon to find the volume of different prisms and area of composite shapes.

In this unit pupils extend their knowledge of shapes by exploring the properties of circles and composite shapes before developing understanding of 3-D shapes including surface area and volume.

Perimeter, area and volume

The surface area is the {{ }} area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces. 

The prism has 6 faces, two are parallelograms and four are rectangles.

The prism has 6 faces, two are trapeziums and four are rectangles.

The prism has 6 faces, two are isosceles triangles and four are rectangles.

Here is a right prism. Which of these descriptions is correct?

The areas of the faces of a triangular prism are $$24\text{ cm}^2,24\text{ cm}^2,50\text{ cm}^2, 40\text{ cm}^2\text{ and }30\text{ cm}^2$$ respectively. The surface area is {{ }} $$\text{ cm}^2$$. 

The surface area of this right-angled isosceles triangular prism is {{ }} $$\text{ cm}^2$$.

In a right prism, the rectangular faces can be seen as one large rectangle. The dimensions of the large rectangle are the {{ }} of the base by the length of the prism.

The area of a rectangle with a width of 7 cm and a length of 12 m is {{ }}m².

The area of a triangle with a base length of 14 cm and a perpendicular height of 8 cm is {{ }} cm². 

The area of a trapezium is being calculated $${\text {Area}}={{1}\over{2}} \times {(6+16)} \times {12} = 132  \text{ cm}^2$$. What is the perpendicular height of this trapezium?

A prism is a polyhedron with a base that is a {{ }} and a parallel opposite face that is identical. The corresponding edges of the two polygons are joined by parallelograms. 

Match the shape of the base with the name of the prism.

Starter Quiz

The area of a rectangle with a width of 7 cm and a length of 12 m is m².