A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.
What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk. Background photo: © Inga Nielsen/iStockphoto.
About This Lesson Plan



20 Mins

Setting the Stage with Geometry

Lesson 2: Surface Area of 3D Shapes

In this lesson, students build knowledge of surface area, and complete related worksheet problems related to painting props for a concert.

In “That Should Cover It!” students will understand formulas used to measure the surface area of these basic three-dimensional shapes: a rectangular prism, a cylinder, and a square pyramid.


Time Required: 20 minutes, plus additional time for worksheets
Getting Started

1. After mastering the area of 2D shapes, students can now learn the formulas to measure 3D shapes.

2. Draw a rectangular prism on the board with these measurements: height = 3 feet, length = 4 feet, and width = 5 feet.

3. Show students the surface area formula for rectangular prisms on the poster: SA = 2 • (lw + lh + wh). Explain to them that the surface area of 3D objects is measured in square units, just like the area of 2D objects, and is the sum of all of the 3D object’s surfaces.

4. Ask students what the surface area is of the shape you have drawn. The answer is 2 • (20 + 12 + 15) = 94 square feet.

5. Now draw a cylinder and mark the dimensions with the radius at 3 feet and the height at 4 feet.

6. Show students the surface area formula for cylinders on the poster: SA = (2 • π • r2) + ( dh) and ask them to calculate the answer to the nearest half foot. As (2 • 3.14 9) + (3.14 • 6 • 4) = 131.88 square feet, the answer is 132 square feet.

7. 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.

8. Show students the surface area formula for square pyramids on the poster, SA = (BA) + 1/2 • Pslant h and ask students 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.

9. Distribute Worksheet 2 Printable (PDF). Tell students they should complete all the questions. 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 • r2) + (π • r • slant)]. Go over all correct answers as a class, referring to the Worksheet Answer Key (PDF).

10. Use the following printables as extensions to Lesson 2:

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