Lesson 14: Surface Area of Right Prisms

Surface Area of Right Prisms

Student Summary

To find the surface area of a three-dimensional figure whose faces are made up of polygons, we can find the area of each face, and add them up!

Sometimes there are ways to simplify our work. For example, all of the faces of a cube with side length $s$ are the same. We can find the area of one face, and multiply by 6. Since the area of one face of a cube is $s^2$ , the surface area of a cube is $6s^2$ .

We can use this technique to make it faster to find the surface area of any figure that has faces that are the same.

For prisms, there is another way. We can treat the prism as having three parts: two identical bases, and one long rectangle that has been taped along the edges of the bases. The rectangle has the same height as the prism, and its length is the perimeter of the base. To find the surface area, add the area of this rectangle to the areas of the two bases.

Visual / Anchor Chart

Standards

Building On

3.MD.5

Recognize area as an attribute of plane figures and understand concepts of area measurement.

3.MD.8

Solve real world and mathematical problems involving perimeters of polygons.

6.G.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. Apply these techniques in the context of solving real-world and mathematical problems.

Addressing

7.G.6

Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles and trapezoids. Solve surface area problems involving right prisms and right pyramids composed of triangles and trapezoids. Find the volume of right triangular prisms, and solve volume problems involving three-dimensional objects composed of right rectangular prisms.

Building Toward

7.G.6