Nets and Surface Area
Aligned to 6.G.A.4 — Common Core State Standards for Mathematics.
What this lesson teaches
A net is a 3-D figure unfolded flat into all its faces. To find surface area, find the area of every face on the net and add them together.
Worked examples
Example 1
A cube with 4 cm edges has 6 square faces. Each face is 4 × 4 = 16 cm², so the surface area is 6 × 16 = 96 cm².
Example 2
A rectangular prism 2 by 3 by 5 has faces of 6, 10, and 15, each appearing twice: 2(6 + 10 + 15) = 62 square units.
Example 3
A net is the box unfolded flat. Counting the areas on the net and adding them gives exactly the surface area — that is why nets are useful.
Practice questions
- A rectangular box is 3 by 2 by 5. Find the total area of all six faces.
- Sketch a net for a cube with edge 2 in and find its surface area.
- A triangular prism has two triangle faces of area 6 each and three rectangle faces of area 10 each. Find the surface area.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Desarrollos Planos y Área Superficial
Un desarrollo plano es una figura tridimensional desdoblada en todas sus caras. Para hallar el área superficial, calcula el área de cada cara del desarrollo y súmalas.
Ejemplo 1: Un cubo con aristas de 4 cm tiene 6 caras cuadradas. Cada cara mide 4 × 4 = 16 cm², así que el área superficial es 6 × 16 = 96 cm².
Ejemplo 2: Un prisma rectangular de 2 por 3 por 5 tiene caras de 6, 10 y 15, cada una dos veces: 2(6 + 10 + 15) = 62 unidades cuadradas.
Ejemplo 3: Una red es la caja desdoblada. Contar las áreas de la red y sumarlas da exactamente el área superficial — por eso sirven las redes.
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