Year 10: Three-dimensional shapes and pyramids

In Year 10 Geometry, you are expected to calculate properties of 3D shapes such as prisms, cylinders, and pyramids. The main focus is understanding faces, edges, and vertices, and then finding surface area accurately.

Surface area means the total area of all outer faces. A net is often the easiest way to organise the calculation.

Reading 3D shapes

Start by identifying the base shape. A prism has the same cross-section all the way through, while a pyramid has triangular faces meeting at an apex.

Surface area of a prism

Example 1: Find the surface area of a rectangular prism with dimensions

4 cm

3 cm

, and

2 cm

There are three pairs of equal faces.
Area $= 2 (4 \times 3) + 2 (4 \times 2) + 2 (3 \times 2)$ .
$= 24 + 16 + 12 = 52 {cm}^{2}$ .

Surface area of a pyramid

For a square pyramid, add the area of the square base and the areas of the four triangular faces.

Example 2: A square pyramid has base side length

6 cm

and slant height

5 cm

. Find the surface area.

Base area $= 6 \times 6 = 36 {cm}^{2}$ .
One triangular face area $= 1 / 2 \times 6 \times 5 = 15 {cm}^{2}$ .
Four triangular faces give $4 \times 15 = 60 {cm}^{2}$ .
Total surface area $= 36 + 60 = 96 {cm}^{2}$ .

Why nets help

A net turns the solid into flat shapes you already know how to measure. This is especially helpful in pyramid questions where students often forget one or more triangular faces.

Example 3: A triangular prism has two triangular ends and three rectangular side faces. A net makes it obvious that all five faces must be included in the final total.

Common mistakes