# 10.1: FOILed Again

*This activity is intended to supplement Algebra I, Chapter 9, Lesson 2.*

## Problem 1 - Introduction to Area of a Rectangle

Run the **AREA** program (in **PRGM**) and select the option for Problem 1 (#1).

Enter 6 for .

1. What are the lengths of the sides of the rectangle?

2. What is the area of the rectangle when ?

Now, change the width of the side by running the program again and enter a new value for .

3. What is the area of the rectangle when ? When ?

4. Explain how the expression for the area is simplified.

## Problem 2 - Areas of Small Rectangles

The rectangle at the right has dimensions and rate of . Each piece of the rectangle is a different color so that you can focus on its area.

5. What is the area of each small rectangle?

6. What is the total area of the rectangle?

## Problem 3 - FOIL Method

Run the **AREA** program and select the option for Problem 3.

Enter for .

7. How do the areas of the small rectangles in Problem 2 relate to the expression shown on the bottom of the screen?

Practice finding the area of a rectangle and then check your answers with the program.

8. What is the expression of the area of a rectangle with dimensions and ?

9. a.

b.

c.

## Homework/Extensions

Practice finding the area. Record your answers here. Show each step of your work. Use the program to check your answer.

1. a.

b.

c.

d.

Next, you will be multiplying a trinomial (3 terms) times a binomial (2 terms) to find the area of a rectangle.

2. What method can you use to find the simplified expression for the area?

3. Use the letters and to determine the formula used to find the 6 terms of area shown at the right.

4. What is the area of the rectangle with dimensions and ?

5. a.

b.

c.