Surface area

Learning Objectives Define surface area and explain its meaning in their own words. Identify the faces of common 3D shapes like rectangular prisms and cubes. Calculate the area of individual rectangular and square faces of a 3D shape. Calculate the total surface area of a rectangular prism using its dimensions. Calculate the total surface area of a cube given its side length. Solve real-world problems involving the surface area of rectangular prisms and cubes. Have you ever wrapped a present 🎁 or painted a box? How much wrapping paper or paint did you need to cover the whole thing? In this lesson, we'll learn about surface area, which is the total area of all the outer surfaces of a 3D shape. Understanding surface area helps us measure how much material is needed to c...

TermDefinitionExample 3D ShapeAn object that has length, width, and height, taking up space in the real world.A shoebox, a dice, a building. FaceA flat surface of a 3D shape.The top, bottom, front, back, left, or right side of a rectangular prism. EdgeThe line segment where two faces of a 3D shape meet.The line where the top face and the front face of a box connect. Vertex (plural: Vertices)A corner point where three or more edges of a 3D shape meet.The corner of a cube where three edges come together. NetA 2D (flat) pattern that can be folded to form a 3D shape.If you cut open a cereal box and lay it flat, that's its net. AreaThe amount of space a 2D (flat) shape covers, measured in square units.The area of a square with sides of 5 cm is 25 square centimeters ($25 \text{ cm}^2$). Su...

Area of a Rectangle $A = l \times w$ To find the area of a rectangular face, multiply its length ($l$) by its width ($w$). This is the first step to finding the surface area of any rectangular face. Area of a Square $A = s \times s$ or $A = s^2$ To find the area of a square face, multiply its side length ($s$) by itself. All sides of a square are equal. 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 its three unique pairs of faces (length × width, length × height, width × height) and add them together, then multiply by 2 because each pair has two identical faces. Surface Area of a Cube $SA = 6s^2$ To find the total surface area of a cube, calculate the area of one square...