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 rectangles below. write an equation for the total area by adding the purple boxes. a.) area = hint: multiply the two sides and add the purple boxes. ignore this box x 3x² 6x

Explanation:

Step1: Calculate area of each sub - rectangle for the first problem

For the rectangle with dimensions \(4x\), \(2x\); \(4x\), \(- 7\); \(3\), \(2x\); \(3\), \(-7\).
The area of a rectangle is length times width.
The areas of the sub - rectangles are:
For the rectangle with sides \(4x\) and \(2x\), the area \(A_1=4x\times2x = 8x^{2}\).
For the rectangle with sides \(4x\) and \(-7\), the area \(A_2=4x\times(-7)=-28x\).
For the rectangle with sides \(3\) and \(2x\), the area \(A_3 = 3\times2x=6x\).
For the rectangle with sides \(3\) and \(-7\), the area \(A_4=3\times(-7)=-21\).

Step2: Find the total area of the first rectangle

The total area \(A\) of the rectangle is the sum of the areas of the sub - rectangles.
\(A = 8x^{2}-28x + 6x-21=8x^{2}-22x-21\).

Step3: Analyze the second rectangle

In the second rectangle, if one side of the rectangle with area \(3x^{2}\) is \(x\), then the other side is \(\frac{3x^{2}}{x}=3x\).
The area of the rectangle with sides \(3x\) and \(6x\div x = 6\) is \(3x\times6 = 18x\).
The total area of the second rectangle is the sum of the areas of the purple - box rectangles.
The areas of the purple - box rectangles are \(3x^{2}\) and \(6x\) and \(18x\).
The total area \(A'=3x^{2}+6x + 18x=3x^{2}+24x\).

Answer:

a.) For the first rectangle: \(8x^{2}-22x - 21\)
a.) For the second rectangle: \(3x^{2}+24x\)