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 W.
1. What are the lengths of the sides of the rectangle?
2. What is the area of the rectangle when w=6?
Now, change the width of the side by running the program again and enter a new value for W.
3. What is the area of the rectangle when w=4? When w=9?
4. Explain how the expression for the area is simplified.
Problem 2 - Areas of Small Rectangles
The rectangle at the right has dimensions (x+7) and rate of (x+2). 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 (x+7)(x+2) for (AX+B)(CX+D). (A=1,B=7,C=1,D=2)
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 (3x+5) and (6x+2)?
9. a. (4x+1)(3x+9)
Practice finding the area. Record your answers here. Show each step of your work. Use the program to check your answer.
1. a. (4x+2)(x+7)=
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 a,b,c,d, and e 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 (1x2+3x+4) and (5x+6)?
5. a. (2x2+1x+7)(3x+(−6))=