Surface Area Worksheets
Free printable surface area worksheets: find the surface area of boxes from their nets and from labelled drawings, with an answer key.
Half the problems on each sheet draw a net, the flat shape a box unfolds into, with its six rectangles laid out in a cross. The other half draw the box itself, with its length, width and height labelled. Each asks for the surface area: the total area of the six faces.
On a net every face can be seen, so the surface area is the six rectangles' areas added up. On a drawing of the box only three faces show, and the student has to know that each hidden face matches the one opposite it, so the surface area is twice the front, twice the top and twice the side.
Each length is a whole number of centimetres, labelled once, and every answer is in square centimetres. The longest edge can be set to 5, 10 or 12 in the settings.
What this worksheet covers
- Find the surface area of a rectangular prism from its net
- Find the surface area of a rectangular prism from its length, width and height
- Use the fact that opposite faces of a box have equal areas
Common Core standards
- 6.G.A.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.
- 7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Frequently asked questions
How do you find the surface area of a box?
Find the area of the front, the top and one side, add them, and double the total, because each face has a matching face opposite it. A box 5 cm long, 3 cm wide and 2 cm high has faces of 5 × 2 = 10, 5 × 3 = 15 and 3 × 2 = 6 square centimetres, so its surface area is 2 × (10 + 15 + 6) = 62 cm².
What is a net?
A net is the flat shape you get by cutting a box along some of its edges and unfolding it. A box's net has six rectangles, in three matching pairs. The nets on these sheets are laid out as a cross, a strip of four faces with one face on each side, which is the layout most textbooks use first.
What is the difference between surface area and volume?
Surface area is the area that covers the outside of a box, measured in square units such as cm². Volume is the space inside it, measured in cubic units such as cm³. The 5 by 3 by 2 box above has a surface area of 62 cm² and a volume of 5 × 3 × 2 = 30 cm³.
Why is each length labelled only once on the net?
Every edge of a face meets an edge of the same length somewhere else in the net, so one label for each of the three lengths is enough, and finding the matching edges is part of reading a net. The labels sit on outside edges, so no number could belong to two faces.