This worksheet gives Grade 6 students ten problems on surface area and nets of cubes, rectangular prisms, triangular prisms, and square pyramids. The problems begin with a single cube and move toward open boxes, missing edges, and solids built from several face shapes.
The last three problems are word problems about gift wrap, paint, and a camping tent. Every problem practices Common Core standard 6.G.A.4. Draw the net when it helps, list every face, and write square units.
Problem 1: Cube net
The net of a cube has six squares with edges of \(5\text{ in}\). Find the surface area of the cube.
Problem 2: Rectangular prism
Find the surface area of a rectangular prism that is \(6\text{ ft}\) long, \(4\text{ ft}\) wide, and \(3\text{ ft}\) tall.
Problem 3: Name the solid
A net is made of 2 triangles and 3 rectangles. Name the solid it folds into and tell how many faces it has.
Problem 4: Triangular prism
Find the surface area of the triangular prism whose net is shown. The triangles have legs \(3\text{ in}\) and \(4\text{ in}\) and the prism is \(10\text{ in}\) long.
Problem 5: Square pyramid
A square pyramid has a base edge of \(6\text{ m}\), and each triangular face has a slant height of \(5\text{ m}\). Find its surface area.
Problem 6: Open-top box
A box has no lid. It is \(10\text{ in}\) long, \(8\text{ in}\) wide, and \(4\text{ in}\) tall. Find the area of the outside surface.
Problem 7: Missing edge
A cube has a surface area of \(216\text{ in}^2\). Find the length of one edge.
Problem 8: Gift wrap
Priya wraps a gift box that is \(12\text{ in}\) long, \(9\text{ in}\) wide, and \(3\text{ in}\) tall. Find the least amount of wrapping paper that covers the whole box with no overlap.
Problem 9: Toy chest paint
Diego paints the outside of a closed toy chest that is \(4\text{ ft}\) long, \(2\text{ ft}\) wide, and \(2\text{ ft}\) tall, including the bottom. One quart of paint covers \(20\text{ ft}^2\) with one coat and costs \(\$9\). Find the surface area, then the cost of the paint for two coats.
Problem 10: Camping tent
A tent is shaped like a triangular prism. Each triangular end has a base of \(6\text{ ft}\) and a height of \(4\text{ ft}\). The two slanted sides are \(5\text{ ft}\) wide, and the tent is \(8\text{ ft}\) long. The floor is included. Fabric costs \(\$2.50\) per square foot. Find the amount of fabric and its cost.
See every chapter on the Grade 6 math page.