L1 · Nets and 2-D models; surface area of right prisms

Learning goal

“I can unfold a right prism into a net, name every face with its dimensions, and find the total surface area by adding the areas of all the faces - remembering that opposite faces of a prism are identical pairs.”

Surface area — the total area of the surface of a 3-D shape: the sum of the areas of every face and curved surface. It answers "how much material covers it," and it is measured in square units.

Net — a flat 2-D arrangement of a shape's faces that folds up into the 3-D shape. A 3-D shape can have several different nets; some flat arrangements are not nets at all (they overlap or leave a gap when folded).

Polyhedron — a 3-D shape whose faces are all polygons. Prisms and pyramids are polyhedrons; cylinders and spheres are not.

Right prism — a polyhedron with two identical, parallel polygonal bases joined by rectangular side faces. A shoebox is a right rectangular prism; its "length" is the distance between the two bases.

Worked example

A cube has edge length 5 cm. Its net is six squares in a cross: one centre square, one attached to each of its four sides, and one more attached below the centre. Step 1: Every face of a cube is the same square: 5 x 5 = 25 cm2. Step 2: A cube has 6 faces - count them on the net: 6 squares, no overlaps, no gaps. Step 3: Surface area = 6 x 25 = 150 cm2. Say it plainly: surface area is a FACE CENSUS - list every face, compute each area, add them all.

Check yourself — explain it

A straight row of six squares is NOT a net of a cube because...

Paired problem — example still visible

Cube with edge 3 cm -> each face 9 cm2 -> SA = 6 x 9 = 54 cm2

Faded completion — last step is yours

"Cube, edge 6 cm: one face = 6 x 6 = ___ cm2; SA = 6 x ___ = ___ cm2" -> 36; 36; 216 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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