Surface area of cubes and rectangular prisms

Learning Objectives Identify the faces, edges, and vertices of cubes and rectangular prisms. Recognize and draw nets for cubes and rectangular prisms. Calculate the area of a single rectangular or square face. Apply the formula to find the surface area of a cube. Apply the formula to find the surface area of a rectangular prism. Solve real-world problems involving the surface area of cubes and rectangular prisms. Ever wondered how much wrapping paper you need for a gift 🎁 or how much paint to cover a toy box? In this lesson, you'll learn how to calculate the total area of all the surfaces of 3D shapes called cubes and rectangular prisms. This skill helps us understand the 'skin' of these objects and is useful in many everyday situations. Real-World Applicat...

TermDefinitionExample CubeA three-dimensional shape with six identical square faces. All edges are the same length.A standard dice or a Rubik's Cube. Rectangular PrismA three-dimensional shape with six rectangular faces. Opposite faces are identical.A shoebox, a brick, or a book. FaceA flat surface of a three-dimensional shape.Each side of a dice is a face. A rectangular prism has 6 faces. EdgeA line segment where two faces of a three-dimensional shape meet.The line where two sides of a box meet. Vertex (plural: Vertices)A point where three or more edges of a three-dimensional shape meet. Also called a corner.The corner of a shoebox. NetA two-dimensional pattern that can be folded to form a three-dimensional shape. It shows all the faces laid out flat.If you cut open a cereal box and...

Area of a Rectangle $A = l \times w$ Use this to find the area of a single rectangular face, where $l$ is the length and $w$ is the width. Area of a Square $A = s \times s = s^2$ Use this to find the area of a single square face, where $s$ is the side length. Surface Area of a Cube $SA = 6 \times s^2$ To find the total surface area of a cube, calculate the area of one square face ($s^2$) and multiply it by 6, since all 6 faces are identical. Surface Area of a Rectangular Prism $SA = 2(lw + lh + wh)$ To find the total surface area of a rectangular prism, calculate the area of each unique pair of faces (length $\times$ width, length $\times$ height, width $\times$ height), add them together, and then multiply by 2 because there are two of each pair.