How to Find the Surface Area of a Composite 3D Figure

Key takeaway: When a problem lists several edge lengths but leaves out the picture, the safest move is to identify the solid first. Surface area is always the sum of all exposed faces, so the shape’s structure matters more than any single number.

To find surface area, you normally:

1. Identify the solid from the diagram.
2. Break it into faces or simpler parts.
3. Add the area of every exposed face.

If this is a prism or a composite solid, the key formula is often:

$SA = \text{sum of all face areas}$

or, for a right prism,

$SA = 2B + Ph$

where $B$ is the area of one base, $P$ is the base perimeter, and $h$ is the height.

Because the figure is not included in the text you provided, the exact numerical surface area cannot be verified from the prompt alone. If you have the diagram, match each labeled length to its corresponding face, then compute each area separately before adding them together.

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Pitfalls the pros know 👇 A common mistake is to multiply every number you see together. That almost never works for surface area. Another trap is counting hidden faces or forgetting that two identical bases may both be exposed. Always check which dimensions belong to the same face.

What if the problem changes? If the figure is actually a rectangular prism, use

$SA = 2(lw + lh + wh)$

If it is a triangular prism, find the triangle area first, then use the prism formula. If you send the diagram, the surface area can be computed exactly instead of only by method.

Tags: surface area, net of a solid, lateral area