PART A
1. Write an expression representing the area of the square in terms of a.
2. Draw a square in the bottom left corner of the large square and call the length b.
3. Write an expression representing the área of the new square in terms of b.
4. Shade everything except the new square with length 6
5. Write an expression representing the área on the shaded part. (HINT: use your answers from 1 and 3)
PART B
1. Extend the line formed for the top of the small square (length &) to the right until it meets the side of the original square. There should now be a rectangle next to the smaller square.
2. What is the rectangle's length and breadth in terms of a and b?
3. Cuto ut the small square and set aside.
4. Cuto ut the rectangle and lay it alongside the leftover part to form a larger rectangle. Make sure there are two sides that are the same length are next to each other. (The rectangle will need to turn).
5. What is the NEW rectangle's length and breadth in terms of a and b?
6. Write an expression representing the area of the new rectangle in terms of a and b. There is no need to simplify- leave it in its original form.
7. What is the relationship between the area of the shaded region (Part A step 5) and the área of new rectangle?
8. What algebraic concept has been proven by this investigation?
