Question

1 - 66. 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. b. area = hint: multiply the two sides and add the purple boxes.

Explanation:

Step1: Analyze part a

The rectangle has dimensions where one side has parts 8 and 10. The area of a rectangle is length times width. The two - part rectangle's area can be found by considering the two sub - rectangles. The first sub - rectangle has area \(10\times8 = 80\) and the second has area \(10\times10=100\). The total area of the rectangle in part a is the sum of these two areas.

Step2: Calculate area of part a

\[A_a=80 + 100=180\]

Step3: Analyze part b

In part b, one side of the rectangle has parts 4 and 12, and the other side has parts 12 and some unknown value related to the purple - box situation. The first sub - rectangle has area \(12\times4 = 48\) and the second has area \(12\times12 = 144\). The total area of the rectangle in part b is the sum of these two areas.

Step4: Calculate area of part b

\[A_b=48+144 = 192\]

Answer:

a. 180
b. 192