Surface Area of Prisms 7.G.6: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Lesson 9.1

Real-Life Connection Gift wrap How is gift wrapping related to surface area?

Surface Area Vocabulary surface area lateral face lateral area lateral surface

Surface Area The sum of the areas of all the surfaces (faces) of a 3D figure. *We use nets (a 2D pattern) to see all the faces of the solid as if it was “unfolded.”

Surface Areas of Prisms Lateral faces of a prism are parallelogram s that connect the bases. Lateral area of a prism is the sum of the areas of the lateral faces. S = 2B + L S = 2B + Ph

Surface Areas of Prisms Use your favorite version of the formula! S = 2B + L, S = 2b + Ph, S = 2lw+2lh+2wh, etc. Mrs. Sun’s personal favorite is: S = 2B + Ph Mrs. Sun’s personal favorite is: S = 2B + Ph Mrs. Sun’s personal favorite is: S = 2B + Ph

Also remember… If you forget the formula You can always find the areas of each face and add the areas together! This is aka “Lateral Surface Area”

Identifying different types of prisms Two identical bases gives the prism its name The other lateral faces should be parallelograms

Example 1 – Finding SA by drawing a net Identify the prism. Find the surface area by drawing a net. (Helps to draw the bases first)

You Try!

Example 2 – Find the SA of a Triangular Prism Find the surface area of the prism. Option: Draw a net (don’t have to) Show your formula to solve Optional net: S = 84 m 2

You Try! SA = 2B + Ph = 204 ft 2 = 2( 8 3) + (18)(10) 1212 Find the surface area of the figure. The figure is a triangular prism.

You Try!

Surface Area of a Cube All edges have the same length S = 6s 2

Example 3

Example 4 Real-life Application

p. 359 #1-3, 8-26 even, 27, 28