Surface Area of Right Rectangular Prisms

Understand how to calculate surface area of rectangular prisms. Alberta Grade 9 geometry lesson with step-by-step examples.

Lesson 1.4 of Square Roots & Surface Area in Grade 9 Math — Alberta curriculum lessons.

What you'll learn in this lesson

• Right Rectangular Prisms?. Understand what a right rectangular prism is and how to calculate its surface area using its dimensions.
• Objects Made from Two Prisms. Explore how combining prisms affects surface area and why some faces become hidden when joined.
• Finding Surface Area of Composite Objects. Follow a step-by-step method to calculate total surface area while removing overlapping or hidden faces.

Inside the lesson — a free preview

1. What Does Surface Area Mean?

Surface Area Definition. Surface area is the total area of all the outer faces of a 3D shape.

2. Surface Area of a Rectangular Prism

A right rectangular prism is a 3D box-shaped object. It has 6 faces — all rectangles — that meet at right angles.

Finding Surface Area. To find its surface area, we add the area of every face:

4. Important Note

💡 Key Points to Remember. Surface area is always measured in square units (like cm², m², or mm²).

1. What Happens When You Join Two Prisms

When two rectangular prisms are connected:. Each prism still has 6 faces,; but some faces overlap where they touch.; Those touching faces are no longer visible from the outside.; To find the true surface area, we do not count those hidden faces.

💡 Think of it like this:. Think of it like gluing two boxes together — the sides that touch the glue are not exposed, so they shouldn't be included in the total area.

3. Step-by-Step Method

📝 General Method. Here's the step-by-step process for any two joined prisms:

1. Determining the Surface Area of Other Composite Objects

What is a Composite Object?. A composite object is an object that is made up of (or composed of) more than one object. It may be composed of more than one of the same type of object such as a "train" of cubes or it can be composed of different types of objects.

Examples of composite objects include:. A "train" of cubes connected in a row; Multiple boxes or prisms joined together; L-shaped or T-shaped objects made from rectangular prisms; Buildings or structures made from multiple box-like components

Worked example: 2. Example – Two Boxes Joined Together

Imagine two rectangular boxes joined side by side.. Prism A: 6 cm × 3 cm × 4 cmPrism B: 4 cm × 3 cm × 4 cm

If they're joined along their 4 cm × 3 cm faces: Each prism has its own surface area, but when joined, the two touching faces (one from each prism) are hidden.; So instead of adding both full surface areas together, we subtract the overlapping faces.

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