Question

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 8
10
40 100
b. area =
hint: multiply the two sides and add the purple boxes.
ignore this box 4 +12
12
24

Explanation:

Step1: Find missing dimensions in part a

In the first row - second column, since one side is 8 and the area of the rectangle is 40, using the formula $A = lw$ (where $A$ is area, $l$ is length and $w$ is width), the other - side is $\frac{40}{8}=5$. In the second row - first column, since one side is 10 and the area of the rectangle is 100, the other - side is $\frac{100}{10}=10$.

Step2: Calculate the total area in part a

The total area of the rectangle is the sum of the areas of the non - ignored boxes. The areas of the non - ignored boxes are 40, 100. Let's assume the missing box in the first row has area $A_1 = 8\times10 = 80$. The total area $A_a=40 + 80+100=220$.

Step3: Find missing dimensions in part b

In the first row - second column, since one side is 4 and the area of the rectangle is 12, using the formula $A = lw$, the other - side is $\frac{12}{4}=3$. In the second row - third column, since one side is 12 (from the value in the first row - third column) and the area of the rectangle is 24, the other - side is $\frac{24}{12}=2$.

Step4: Calculate the total area in part b

The areas of the non - ignored boxes are 12, 12, 24. Let's assume the missing box in the first row has area $A_2 = 4\times12 = 48$. The total area $A_b=12 + 48+24=84$.

Answer:

a. area = 220
b. area = 84