Lesson: Surface Area of Pyramids and Prisms

Engagement (Warm- Up) 5 min.:
How many faces does a square prism have?
How many faces does a square pyramid have?

Exploration (Notes) 15 min.:
Surface Area is the total area of all the faces of a solid figure.

You are doubling the area of the parallel sides.
In essence, you can examine the figure having a Top, Bottom, and sides.

For pyramids, there is only a bottom/ base and sides (which are all triangles).

Square / rectangular prism: 2LW + 2LH + 2WH (square units)
Triangular prism: 2(1/2)(b)(h) + 3(b)(l)
Square: (L)(W) + 4(1/2)(w)(H)
Triangular pyramid: 5(1/2)(b)(h)

Explanation (Instructional) 30 min.:
Teacher will display a cube that has a length of 2in.
SA= 2(4)in.sq. + 2(4)in.sq. + 2(4) in.sq.
SA= 24in. squared

Teacher will display a sqaure pyramid that has a length of 5 ft. and a height of 10 feet.

Teacher can ask the students about the formula for square pyramids and why it differs from cubes, referring back to the warm up. Based on the formula, what should we do to find the surface area of the square pyramid?

SA= (5)(5) + (4)1/2(5)(10)
SA= 25+ 100
SA= 125 ft. sq.

1) You take the Area of the base, which is the sqaure (5x5).
2) You find the area of one of the triangles (1/2)(5)(10).
3) You add the area of the base to the total area of all four triangles (sides) (25+100=125).

Now students must break into groups and try to find the area of each of the figures they created.

Teacher will allow each group 15 minutes to measure and collaborate.

Once the time is up, each group will present their findings on a different sqaure.
Teacher will give confirmation of correct answers.

Elaboration (Independent) 15 min.:
  Homework: Surface Area WKST

Evaluation (Closing) 10 min.:
Exit ticket:
What is the surface area if a triangular prism that has a base of 8in. and a height of 10 in. and a length of 2 in.?