Question

a rectangle has side lengths of 11 and 47. below is the rectangle split into two small rectangles.
(a) find the missing length, and then find the areas (in square units).
(b) use the figure to find 11×47.

Explanation:

Step1: Find the missing length

Since the large - rectangle has a length of 47 and one part of the length of the split - rectangles is 7, the missing length is $47 - 7=40$.

Step2: Calculate the area of the blue rectangle

The area of a rectangle is $A = l\times w$. For the blue rectangle with length 40 and width 11, the area $A_1=11\times40 = 440$.

Step3: Calculate the area of the pink rectangle

For the pink rectangle with length 7 and width 11, the area $A_2=11\times7 = 77$.

Step4: Calculate 11×47

The product $11\times47$ is the sum of the areas of the two small rectangles. So $11\times47=A_1 + A_2=440+77 = 517$.

Answer:

(a) Missing length: 40, Area of blue rectangle: 440, Area of pink rectangle: 77
(b) 517