---
title: "Surface Area of Solids"
description: "Find the surface area of prisms and pyramids by unfolding them into nets of rectangles and triangles, working out each face's area and summing them; apply this to practical problems like wrapping boxe"
canonical: https://lightmysky.com/learn/mathematics/surface-area-of-solids-mt_hdhmurUndc
source: https://lightmysky.com/learn/mathematics/surface-area-of-solids-mt_hdhmurUndc.md
retrieved: 2026-10-19
---

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# Surface Area of Solids

Find the surface area of prisms and pyramids by unfolding them into nets of rectangles and triangles, working out each face's area and summing them; apply this to practical problems like wrapping boxes or painting walls

Subject: Mathematics · Area: Geometry · Ages 11 to 13
Page: https://lightmysky.com/learn/mathematics/surface-area-of-solids-mt_hdhmurUndc

## Ready when they can

- Draw or identify the net of a cuboid, prism, or pyramid and label the dimensions of each face
- Calculate the area of every face and add them to find the total surface area (e.g., a 3 cm × 4 cm × 5 cm box)
- Solve a practical surface-area problem (e.g., how much card is needed to build a model, with the right units)

## Lesson: Surface Area: Adding Up Every Face

Surface area is the total area of every face on the outside of a solid, like a prism or a pyramid. To find it, imagine unfolding the solid flat into its net. Each face becomes a simple shape, a rectangle or a triangle, and you already know how to find the area of those.

**Example.** Take a box that is 3 cm by 4 cm by 5 cm. Unfolded, it has three pairs of matching rectangles: 3 cm x 4 cm, 3 cm x 5 cm, and 4 cm x 5 cm. Their areas are 12 cm2, 15 cm2, and 20 cm2. Since each shape appears twice, the total surface area is 2 x (12 + 15 + 20) = 94 cm2.

*(drawing: Add every face area, remembering the hidden ones too.)*

**Tip.** Always check you have counted every face, including the ones you cannot see, like the bottom and the back. Keep your units the same throughout, such as all in cm2, so nothing gets mixed up.

**Recap.** Unfold the solid, find the area of each face, and add them all together in matching units.

## Practice

14 questions on this page, each with its working shown.

## Needs first

- [Area of Triangles & Parallelograms](https://lightmysky.com/learn/mathematics/area-of-triangles-and-parallelograms-mt_ML5t7n2-U8)
- [3-D shapes (age 11+)](https://lightmysky.com/learn/mathematics/3-d-shapes-age-11-mt_nRksLqt-iR)
- [Nets of 3-D Shapes](https://lightmysky.com/learn/mathematics/nets-of-3-d-shapes-mt_vnJEztczji)

## Opens up

- [Volume and Surface Area of Prisms and Cylinders](https://lightmysky.com/learn/mathematics/volume-and-surface-area-of-prisms-and-cylinders-mt_JTLJ5LDrYh)
- [Similar Shapes: Area and Volume Scale Factors](https://lightmysky.com/learn/mathematics/similar-shapes-area-and-volume-scale-factors-mt_v37c_AeLQa)