Question

TITLE: MODEL MAKING DESCRIPTION: This activity involves the creation of a solid figure out of a given plane figure and expressing it in terms of factors of a polynomial



DIRECTIONS:

1. Create a solid figure from the rectangular figure that was provided by following the steps given.

Step 1. Cut out 2-inches by 2-inches squares in all edges of a 12 inches by 6 inches rectangle.

Step 2. Fold all the sides upward.

Step 3. Paste tape the edges of the new figure.




2. Write your answer to the following questions in a separate sheet. 5 points in each question

a. What is the area of the original rectangle if its side is x units?

b. If the sides of the small squares is y, what expression represents its area?

c. How will you express the area of the new figure in terms of the variables stated in letters a and b? ​

Answer 1

Answer:

• See below

Step-by-step explanation:

Part 1

We had a rectangle with dimensions 12 in x 6 in

We cut 2 in x 2 in squares from each corner and fold up.

We end up with the rectangle with dimensions:

• 12 - 2*2 = 8 in and
• 6 - 2*2 = 2 in

Part 2

a) It gives us one side which is x. If we assume x is the length, then the width is x - 6.

The area is:

• A = lw
• A = x(x - 6) = x² - 6x

b) The small square with side of y, has an area:

• A = y²

c) We subtract the side length of y from the both sides.

The sides of smaller rectangle are:

• l = x - 2y
• w = x - 6 - 2y

The area:

• A = lw =
• (x - 2y)(x - 6 - 2y) =
• x² - 6x - 2xy - 2x + 12 + 4y² =
• x² - 8x - 2xy + 4y² + 12