Surface Area and Volume • Topic 6 of 7

Prisms

A prism is a solid with two identical parallel bases joined by flat faces; a rectangular box is a prism with rectangular bases. Its volume is the base area times the height (length). Its surface area is the sum of the areas of all its faces — for a rectangular box, that is 2(lw + lh + wh), counting the three pairs of opposite faces. For a 4 by 3 by 2 box, the surface area is 2(12 + 8 + 6) = 52. Find each pair of faces, add, and double. The SAT uses prism surface area in wrapping, painting and packaging contexts; keep it separate from volume.

An oblique rectangular prism with its facesPrism (surface area)lhwSurface area = 2(lw + lh + wh)

✅ Solved examples

1. A box is 4 by 3 by 2. Find its surface area.
2(12 + 8 + 6) = 2 × 26 = 52.
2. A box is 5 by 4 by 3. Find its surface area.
2(20 + 15 + 12) = 2 × 47 = 94.
3. A cube of edge 3 is a prism. Find its surface area.
6 × 9 = 54.
4. A box is 6 by 2 by 2. Find its surface area.
2(12 + 12 + 4) = 2 × 28 = 56.

✏️ Practice — try these, take hints as needed

1. A box is 3 by 3 by 2. Find its surface area.
2(lw + lh + wh).
2(9 + 6 + 6).
—
42.
2. A box is 5 by 4 by 2. Find its surface area.
2(20 + 10 + 8).
—
—
76.
3. A box is 4 by 4 by 4. Find its surface area.
6 × 16.
—
—
96.
4. A box is 6 by 3 by 2. Find its surface area.
2(18 + 12 + 6).
—
—
72.
5. A box is 2 by 2 by 5. Find its surface area.
2(4 + 10 + 10).
—
—
48.

📝 Topic test — 8 questions

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