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Surface area of a rectangular prism worksheets

A box has six faces in three matching pairs, so its surface area is twice the front plus twice the side plus twice the top. These free printable worksheets ask for it straight from the solid, cut from the surface area and nets page.

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Surface area of a rectangular prism
Surface area of a rectangular prism worksheet — Edges to 20 cm, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The surface area and nets page shows the box, its unfolded net, or both; this sheet keeps only the closed solid, so a child practices holding the three hidden faces in mind rather than reading them off a flat cross. It is the harder half of that page, worth its own set once the net has done its teaching.

Why this sheet works

Only three numbers appear on the drawing, and that is the work: six faces come in three matching pairs, so the long addition collapses to 2(lw + lh + wh). Children who have just finished volume will often multiply all three numbers together instead — the confusion this practice exists to sort out.

How this one works

One question from this sheet, worked through a step at a time.

Surface area of a 4 × 5 × 12 box

4 × 5 × 12 cm
front and back:2 × 4 × 12 =96
front and back:2 × 4 × 12 =96
the two sides:2 × 5 × 12 =120
front and back:2 × 4 × 12 =96
the two sides:2 × 5 × 12 =120
top and bottom:2 × 4 × 5 =40
front and back:2 × 4 × 12 =96
the two sides:2 × 5 × 12 =120
top and bottom:2 × 4 × 5 =40
total:256
  1. Six faces, and the drawing can only show you three of them. The three you cannot see are the reason the usual wrong answer here is five faces added perfectly.
  2. Front and back are 4 by 12, and they are identical — so that pair is 2 × 4 × 12 = 96.
  3. The two sides are 5 by 12, and they are identical — so that pair is 2 × 5 × 12 = 120.
  4. Top and bottom are 4 by 5, and they are identical — so that pair is 2 × 4 × 5 = 40.
  5. Three pairs, six faces, none missed: 96 + 120 + 40 = 256 square cm.

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