Surface Area of Cuboids – SA = 2(lw + lh + wh)
A cuboid's 6 faces come in 3 matching pairs: a top and bottom (each l × w), a front and back (each l × h), and two sides (each w × h). Adding up all 6 faces gives the formula SA = 2(lw + lh + wh) – the 2 accounts for each pair appearing twice.
Breaking the formula down face-pair by face-pair, rather than memorising it as one block, makes it much easier to adapt when you only need part of the total – for example, finding the area of just one face, which is a common building-block skill for later composite-shape and open-box problems.
Calculating a Cuboid's Surface Area
SA = 2(lw + lh + wh). Each of the three terms represents one pair of matching faces.
Find the surface area of a cuboid 8 cm × 3 cm × 4 cm.
SA = 2(8×3 + 8×4 + 3×4) = 2(24 + 32 + 12) = 2 × 68 = 136 cm².
Real-Life Application
- Box manufacturing: calculating cardboard needed for boxes of different sizes.
- Wallpapering: finding the wall area of a room shaped like a cuboid.
- Aquariums: calculating the glass needed for a fish tank.
Key Takeaways
- A cuboid's surface area formula is SA = 2(lw + lh + wh).
- The three terms correspond to the three pairs of matching faces.
- Individual face areas (like l × w) are useful building blocks on their own.
Practice: Surface Area of Cuboids
Surface Area of Cuboids
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