### Lesson Plan

# Calculating Surface Area of 3-D Shapes

Students will practice using formulas to measure the surface area of basic 3-D shapes: a rectangular prism, a cylinder, and a square pyramid.

Grades

6–8

Duration

30 MINUTES

### Objectives

**Students will:**

- Understand formulas used to measure the
*surface area*of these basic 3-D shapes: a rectangular prism, a cylinder, and a square pyramid

### Materials

- Setting the Stage With Geometry Worksheet: That Should Cover It! printable
- Setting the Stage With Geometry Reference Sheet: Perimeter, Area, Surface Area, and Volume printable
- Answer Key: Setting the Stage With Geometry printable
- Setting the Stage With Geometry Classroom Poster printable
**Optional:**That's A Wrap! Bonus Worksheet printable**Optional:**Setting the Stage With Geometry Take-Home Activity: Covering Up! printable

### Set Up

- Make class sets of the Setting the Stage With Geometry Worksheet: That Should Cover It! printable and the Setting the Stage With Geometry Reference Sheet: Perimeter, Area, Surface Area, and Volume printable.
- Print a copy of the Answer Key: Setting the Stage With Geometry printable.
- Hang a copy of the Setting the Stage With Geometry Classroom Poster printable in your classroom or project it using a computer and projector.
**Optional:**Make class sets of the Setting the Stage With Geometry Take-Home Activity: Covering Up! printable and the That's A Wrap! Bonus Worksheet printable for students to complete as part of the Lesson Extensions.

### Lesson Directions

### Introduction to Formulas for Surface Area

**Step 1: **Draw a rectangular prism on the board with these measurements: height = 3 feet, length = 4 feet, and width = 5 feet. Ask students to calculate the area of one of the surfaces, say 5 x 4 = 20 square feet. Repeat for the other surfaces. Point out that opposite surfaces have the same area.

**Step 2:** Show students the surface area formula for rectangular prisms on the Setting the Stage With Geometry Classroom Poster: *SA*= 2 (*l • w *+ *l • h *+ *w • h*). Explain to them that the *surface area *of 3-D objects is measured in square units, just like the area of 2-D objects, and is the sum of all of the 3-D object's 2-D surfaces.

**Step 3:** Demonstrate how to calculate total surface area for the rectangular prism you have drawn. The answer is 2 • (20 + 12 + 15) = 94 square feet.

**Step 4: **Now draw a cylinder and mark the dimensions with the radius at 3 feet and the height at 4 feet. Indicate that the surface area for a cylinder equals the area of the two bases plus the area of the surface between the bases. Demonstrate this to your class by using a rolled-up piece of paper to create a cylinder; use two paper circles (cut out beforehand) to fill in the bases. When you unroll the paper, students will see that the surface between the two bases is a rectangle when "unrolled" and that the formula simply adds the area of the bases to the area of the rectangle.

**Step 5: **Show students the surface area formula for cylinders on the Setting the Stage With Geometry Classroom Poster, *SA*= (2 • π • *r ^{2}*) + (

*d • h*), and demonstrate how to calculate surface area for the cylinder you have drawn. The answer is (2 • 3.14 • 3

^{2}) + (3.14 • 6 • 4) = 131.88 square feet.

**Step 6: **Finally, draw a square pyramid on the board and mark the dimensions with a base length of 6 feet and a base width of 6 feet. Show the slant height as 5 feet by drawing a perpendicular line from the center of one of the base sides to the top of the pyramid. The square pyramid has a base area (*BA*) measurable by *l • w *like any square or rectangle.

**Step 7: **Show students the surface area formula for square pyramids on the Setting the Stage With Geometry Classroom Poster, *SA*= (*BA*) + 1/2 *P • slant h*, and show students how to calculate the answer. This formula adds together the area of the base with the area of the four triangular sides of the square pyramid. The *P *in the formula refers to the perimeter of the *base*. The answer is 36 + 1/2 • 24 • 5 = 96 square feet.

### Guided Practice

**Step 8: **In groups or in pairs, ask students to calculate surface areas for:

**A rectangular prism with the following measurements: length 3 meters, width 7 meters, and height 5 meters.**2(3 x 7 + 5 x 7 + 3 x 5) = 142 square meters.**A cylinder with a radius of 6 feet and a height of 10 feet.**2 x 3.14 x 6^{2}+ 3.14 x 12 x 10 = 602.88 square feet, rounded to the nearest hundredth.**A square pyramid with one side of the base 60 meters long and a slant height of 50 meters.**The area of the base is 60 x 60 = 3,600 meters. The perimeter of the base = 4 x 60 = 240 meters. The surface area of the square pyramid is 3,600 + 1/2 x 240 x 50 = 9,600 square meters.

### Independent Practice

**Step 9:** Distribute the Setting the Stage With Geometry Worksheet: That Should Cover It! printable. Tell students they should complete all the questions.

**Note:** You may want to take some extra time in class to go over the bonus question, which introduces the formula for measuring the surface area of a cone: *SA*= (π • *r*^{2}) + (π • *r • slant*).

**Step 10: Check for Understanding:** Go over all correct answers as a class, referring to the Answer Key: Setting the Stage With Geometry printable.

### Supporting All Learners

Provide the Setting the Stage With Geometry Reference Sheet: Perimeter, Area, Surface Area, and Volume printable for students who are having trouble remembering which formulas go with which polygon.

### Lesson Extensions

Use the following printables as extensions for this lesson:

- Setting the Stage With Geometry Take-Home Activity: Covering Up! printable
- That's A Wrap! Bonus Worksheet printable

### Standards

**Grade 7:**Geometry (CCSS**Grades 6–8:**Make Sense of Problems, Reason Abstractly and Quantitatively, Construct Viable Arguments, Attend to Precision, and Look for and Make Use of Structure (CCSS MP1-3 and 6-7); NCTM

For more information, download the comprehensive Standards Chart: Geometry printable.