How much paper does it take to wrap a box? Unfold boxes into flat nets, find the area of every face and add them up. Play, solve missions and beat the clock.
Start here. The surface area of a solid is the total area of all its faces. Think of the paper you need to wrap a gift. If you cut the paper to fit exactly, with no gaps and no overlaps, the amount of paper is the surface area.
Nets. A net is the box unfolded flat. A box (a cuboid) has 6 faces: Top, Bottom, Front, Back, Left and Right. On the net you can see all six at once, and you can count the little unit squares on each face.
Faces come in pairs. Top and Bottom are the same size, Front and Back are the same size, and Left and Right are the same size. So you only need three areas: length × width, length × height and width × height.
The short way. Surface area of a box = 2 × (l × w + l × h + w × h). For a box 3 cm long, 2 cm wide and 4 cm high: 2 × (6 + 12 + 8) = 52 cm². A cube with side s has 6 equal square faces, so its surface area is 6 × s × s.
Units. Area is measured in square units such as cm². Volume (the space inside) is measured in cubic units such as cm³. They are different things: a box can have a small surface area and a big volume, or the other way round.
Missing faces and prisms. A box with no lid has only 5 faces, so take the lid away from the total. A triangular prism has 2 triangle faces and 3 rectangle faces. For a right-angled triangle with sides a, b and c, and a prism of length L, the surface area is 2 × (½ × a × b) + (a + b + c) × L.
Try this above. In the workshop change l, w and h and watch the six faces. Press "Fold into a box" and then "Unfold into a net". Then try the Wrap-It Puzzles and find the box that needs the least paper.
Surface area is how much paper covers the outside, measured in cm². Volume is how much space is inside, measured in cm³. They are different, so they must never be mixed up.
Every face of a box has an opposite face of exactly the same size. Top and Bottom match, Front and Back match, and Left and Right match. So we add three areas and then double the sum.
Yes. For example a 1 × 2 × 3 box and a 1 × 1 × 5 box would not match, but other pairs of sizes can. The "Wrap exactly" puzzles accept any box that works, so there is often more than one answer.
Pick the level, not the age. "Just starting" counts unit squares on a net. "I know the basics" finds each face area and adds them up. "Challenge me" finds missing sides, handles boxes with a missing face and wraps triangular prisms.
No. It is free and needs no account. Your stars are saved in your own browser.