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# Surface area of a triangular prism
- URL: https://www.esheets.io/surface-area-of-a-triangular-prism/
- Published: 2026-01-07T18:42:24.000Z
- Updated: 2026-06-21T16:47:17.000Z
- Author: Richard Linnington
- Tags: Maths, Geometry and Shape

Calculating the surface area of a triangular prism is a key skill for architects designing A-frame roofs and engineers creating unique packaging, like chocolate boxes. It allows us to measure the exact amount of material needed to cover every side of the 3D shape. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise surface area of a triangular prism with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Identifying the rectangular faces and triangular ends.
- Finding the area of each face.
- Adding all face areas.
- Giving the total surface area in square units.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

## Topic guide

### What this worksheet practises

This worksheet provides practice on calculating the total surface area of a triangular prism (a "Toblerone" shape). This is often considered the hardest basic 3D shape because it is made of five faces that use different formulas: two triangles and three rectangles.

### Key method

You must systematically calculate the area of all five faces and add them together.

- **The Two Triangles:** Calculate the area of the triangular front face using *(base × vertical height) ÷ 2*. Because there is an identical triangle at the back, you then multiply this answer by 2\. (Shortcut: Just do base × height!).
- **The Bottom Rectangle:** Calculate the area of the flat rectangular base the shape sits on (Length × Width).
- **The Sloping Rectangles:** Calculate the area of the large sloping rectangular side(s). You will need the length of the sloping edge of the triangle to do this. (Sloping edge × length of prism).
- Add all five areas together.

### Worked example

**A prism has a triangular front face with a base of 6cm, a vertical height of 4cm, and two sloping edges of 5cm each. The length of the prism is 10cm. Find the surface area.**

Step 1: The two triangles (front and back).

Front area = (6 × 4) ÷ 2 = 12\.   
Back area = 12\.   
Total for triangles = 24.

Step 2: The bottom rectangle.

Base width is 6, length is 10\. Area = 6 × 10 = 60.

Step 3: The two sloping rectangles.

Sloping edge is 5, length is 10\. Area = 5 × 10 = 50\.   
Because it's an isosceles triangle, the other sloping side is also 50\. Total for slopes = 100.

Step 4: Add them all together.

24 (triangles) + 60 (bottom) + 100 (slopes) = 184.

Total surface area = 184 cm².

### Common mistakes to avoid

The biggest mistake is using the vertical height of the triangle to calculate the area of the sloping rectangular sides. The vertical height (e.g. 4cm) is *only* used for the area of the triangle itself. The sloping sides are physical rectangles, and you must use their physical sloping length (e.g. 5cm) to find their area.

### Things to remember

If the front triangle is a right-angled triangle (like a wedge doorstop), the three rectangles will all be completely different sizes. You will have a bottom rectangle, a vertical back rectangle, and one large sloping rectangle on the front. Calculate all three individually.