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

SUBJECT
Math, Geometry

GRADE
6-8

DURATION
20 Mins

COLLECTION
Setting the Stage with Geometry

Lesson 1: Perimeter and Area of 2D Shapes

In this lesson, students build knowledge of perimeter and area, and complete related worksheet problems related to building a stage for a concert.

OBJECTIVE
In ”Geometry Works! The Stage Takes Shape,” students will understand the formulas that measure the perimeter and area of these basic two-dimensional shapes: rectangles, circles, and triangles.

MATERIALS

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

1. Review with students the concept of perimeter. Perimeter is the total distance around the outside of a polygon (a closed figure made up of line segments).

2. On the board, draw a rectangle labeled with a length of 4 feet and width of 3 feet. Then draw a right triangle with a base of 4 feet, height of 3 feet, and hypotenuse (the side opposite the right angle) of 5 feet. Explain that to measure the perimeter of any polygon, you add together the lengths of each side.

3. Ask students what the perimeter of the rectangle is. Show students the formula for the rectangle’s perimeter on the poster and ask why it’s correct. The formula of P (perimeter) = 2 • (l + w) is correct because a rectangle has two sets of sides that are each of equal length. The perimeter of this rectangle is 2 • (4 + 3) = 14 feet.

4. Ask what the perimeter of the triangle is. Show them the formula: P = side a + side b + side c. The perimeter is 3 + 4 + 5, or 12 feet.

5. Tell students that triangles can be classified by angles in three ways: 1) right triangles with one 90° angle where the base and height meet; 2) acute triangles with all angles less than 90°; and 3) obtuse triangles with one angle greater than 90°. The angles of any triangle equal 180°.

6. Draw a circle on the board. Draw a line from the center of the circle to the edge and mark it as 3 feet. Tell students that this is the radius. Ask them what the diameter is. (The answer is 6 feet.) Then explain that the length of the line that forms the circle is called the circumference. There is a unique formula for calculating the circumference: C (circumference) = π • d (diameter). Tell students that π is the circumference of any circle divided by its diameter and equals a number with an infinite decimal: 3.14159.... The decimal continues on infinitely, but to solve most math problems, people use a rounded ratio of 3.14. Ask students to figure out the circumference of the circle you have drawn. Ask them to provide the answer to the nearest half foot. As 3.14 • 6 = 18.84 feet, the answer is 19 feet.

7. Now go over the definition of area on the poster: the measure of a bounded region of a two-dimensional shape expressed in square units, e.g., square inches or square feet. Show your students the formula for area of a rectangle: A (area) = l • w. Ask them to calculate the area of the rectangle you had drawn earlier (4 • 3 = 12 square feet).

8. Now point out the formula for the area of a triangle on the poster: A = 1/2 • [b (base) • h (height)]. Refer back to your drawing of a right triangle with a base of 4 feet and height of 3 feet. Ask students to calculate the area. The answer is 1/2 • (4 • 3) = 6 square feet.

9. Finally, go over the area formula for circles. Again, refer to the poster: A = π • r2, where r2 means radius squared, or r • r. The answer is π (3.14) • r2 (3 • 3) = 28.26 square feet. Ask students to provide the answer to the nearest half foot. The answer is 28.5 feet or 28 feet and 6 inches.

10. Distribute Worksheet 1 Printable (PDF). Tell students they should complete all the questions. Explain that the bonus question introduces a new formula for the area of trapezoids. Go over correct answers as a class using the Worksheet Answer Key (PDF) .

11. Use the following printables as extensions to Lesson 1:


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