L1 · Surface Area of Right Prisms

Learning goal

“I can find the surface area of any right prism by unfolding it into a net: two congruent bases plus one rectangle for each side face - and I only count the faces the problem actually has (an open top has no lid).”

Surface area — the total area of all the faces of a 3-D object, in SQUARE units (cm2, m2, ft2). It answers "how much material covers it?"

Right prism — a solid with two congruent, parallel polygon bases and rectangle side faces standing straight up from the base edges. (A cardboard box is a right prism whose base is a rectangle.)

Net — the flat pattern you get by unfolding a solid. Every face of the solid appears exactly once in the net.

Lateral faces — the rectangle side faces of a prism - everything except the two bases.

Worked example

Sketch and label first (always). A rectangular prism measures 8 cm by 5 cm by 3 cm. Find its surface area. Step 1: List the face pairs from the net. Front/back: 8 x 5 = 40 cm2 each. Top/bottom: 8 x 3 = 24 cm2 each. Ends: 5 x 3 = 15 cm2 each. Step 2: Add one of each, then double: 40 + 24 + 15 = 79 cm2. Step 3: SA = 2 x 79 = 158 cm2. Sanity check: six faces, the biggest is 40 - a total between 100 and 200 is reasonable. Formula form: SA = 2(lw + lh + wh) for length l, width w, height h.

Check yourself — explain it

Why is the "add then double" move legal here?

Paired problem — example still visible

Prism 7 cm by 2 cm by 4 cm -> 2(14 + 28 + 8) = 2 x 50 = 100 cm2

Faded completion — last step is yours

"Prism 9 cm by 6 cm by 2 cm: SA = 2(54 + 18 + 12) = 2 x 84 = ___ cm2" -> 168 cm2

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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Grade 10 — Mathematics 10C › C10U02 Surface Area & Volume

L1 · Surface Area of Right Prisms