Surface Area of Solids

Pre-Algebra · Axiom Academy

Unfold a 3D shape into a flat net and the surface area is just the sum of all the face areas. To measure surface area we don't have to fight with a 3D picture. We unfold the solid until every face lies flat on the table. That flat pattern is the net — and the surface area is simply the sum of the areas of the pieces you see. A cube has 6 identical square faces . Watch it unfold into a cross of six squares — then every face is just . With side , each face is , and the six of them add to the surface area. six equal squares, so multiply one face by 6 A box has 6 rectangular faces in 3 matching pairs : top & bottom, front & back, and the two side faces. As it unfolds, each pair has equal area — find one of each and double it. Here the box is . three pairs: lw , lh , and wh , each counted twice 4. The Triangular Prism & the General Strategy A triangular prism unfolds into 2 triangular ends and 3 rectangular sides . With a right-triangle end (legs 4 and 3 ) and length , watch the five faces fold out flat and add up. Unfold (or picture the net) and count the faces and their shapes — squares, rectangles, triangles. Use the right formula per face: square s^2 , rectangle , triangle . Sum the face areas. That total is the surface area. Make sure no face was missed and the units are square units ( , ). You've seen that every surface-area problem is the same move: unfold the solid into its net and add up the face areas. Scroll up to replay any unfolding.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.