Surface Area of Composite Objects

Learn to find surface area of composite 3D objects. Alberta Grade 9 math with visual examples and practice problems.

Lesson 1.5 of Square Roots & Surface Area in Grade 9 Math — Alberta curriculum lessons.

What you'll learn in this lesson

• Review: Area Formulas. Review the fundamental area formulas for rectangles, squares, circles, and triangles before tackling composite objects.
• Mixed Shape Composite Objects. Learn to find surface area of objects made from different shapes like triangular prisms, rectangular prisms, and cylinders.
• Practice Problems. Apply your knowledge to solve challenging composite object problems with step-by-step solutions.

Inside the lesson — a free preview

Step 1: What objects make up this whole object?

A triangular prism A rectangular prism

Step 2: Find the surface area of each object.

↳ surface area of triangular prism. = 2 triangles + 3 different rectangles

↳ surface area of rectangular prism. = 2 × front + 2 × right side + 2 × top

Step 3: Find the area of the overlap. Don't forget to double it!!

Overlap = (ℓ × w).

❗ Why do we double the overlap?. When two objects are joined together, TWO surfaces are hidden:

Step 4: Find the total surface area of the composite object.

Total surface area =. SA of triangular prism + SA of rectangular prism - overlap

Practice Problem: Find the Surface Area of the Composite Object Shown

PLEASE TRY THIS QUESTION ON YOUR OWN BEFORE LOOKING AT THE SOLUTION

Step 1: What objects make up this whole object?

Split into two rectangular prisms. From the diagram, we can identify two rectangular prisms:

Step 2: Find the surface area of each object.

↳ surface area of Prism A. SA = 2(lw + lh + wh)

↳ surface area of Prism B. SA = 2(lw + lh + wh)

Step 3: Find the area of the overlap. Don't forget to double it!!

Contact face dimensions. Where the prisms join, one face from each prism becomes hidden.

❗ Why do we double the overlap?. When two objects are joined together, TWO surfaces are hidden:

Step 4: Find the total surface area of the composite object.

Total surface area =. SA of Prism A + SA of Prism B - overlap

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