# 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**

- Worksheet 1 Printable (PDF)
- Extension: Bonus Worksheet 1 Printable (PDF)
- Extension: Take-Home Activity 1 (PDF)
- Resource: Formula Chart (PDF)
- Resource: Mini-Poster (PDF)

**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:

- Extension:
**Bonus Worksheet 1 Printable (PDF)** - Extension:
**Take-Home Activity 1 (PDF)**

**Program Links: **