Question

1 - 36 do problem 1 - 37 before this one. write an expression for the area of the rectangle below. a.) area = hint: add the boxes after multiplying terms.

	2x	- 7
4x
3

1 - 47 area model puzzles fill in the area of the missing dimensions and areas of the rectangle. write an equation for the total area by adding the purple boxes. a.) area = hint: multiply the two sides and add the purple boxes.

	x
3x²	6x

Explanation:

Step1: Recall area formula for rectangle

The area of a rectangle is $A = l\times w$ (length times width). For the first rectangle with dimensions split as such, we multiply the terms in the rows and columns and sum them up.

Step2: Calculate area of first rectangle

We have two - row and two - column rectangles. For the first one, multiplying the terms:
The area is $(4x)(2x)+(4x)( - 7)+(3)(2x)+(3)( - 7)=8x^{2}-28x + 6x-21=8x^{2}-22x - 21$.

Step3: Analyze second rectangle

For the second rectangle, if we assume the length and width are composed of the given terms. Let's say the length and width are expressions that when multiplied give the sum of the areas of the sub - rectangles. If we consider the structure, assume the factors of the quadratic terms. Since we have $3x^{2}$ and $6x$, and one side has a factor of $x$. Let the other side be $3x + 6$. Then the area of the rectangle is $x(3x + 6)=3x^{2}+6x$.

Answer:

a) $8x^{2}-22x - 21$
b) $3x^{2}+6x$