Question

The rectangle to the left is divided into 12 shapes. One of them is a rectangle labeled with #1 and the remaining 11 shapes are squares. The length of the side of each one of the shaded squares is 1 ft. Find the area of the given rectangle.

Answer 1

The problem is as shown in figure
calculating the dimension of all rectangle as follow:
The rectangle consisting of squares except the shape labeled #1
∵ The length of the side of each one of the shaded squares is 1 ft.
∴ The length of side A = 2
And, The length of side B = A +1 =2 + 1 = 3
And, The length of side C = B + 2 = 3 + 2 = 5
And, The length of side D = C + 1 = 5 + 1 = 6
And, The length of side E = A + 1 = 2 + 1 = 3
And, The length of side F = E = 3
And, The length of side G = F = 3

So, The height of required rectangle = C + D = 5 + 6 = 11
And, The width of required rectangle = D + F + G = 6 + 3 + 3 = 12
Then,
The area = height * Width = 11 * 12 =132 ft²

Answer 2

the complete question in the attached figure

Step 1
assign names to different squares

Step 2
calculate the dimensions of each of the squares, starting with those that are close to the unit squares

so
square C=2*2-----> 4 ft²
square G=3*3-----> 9 ft²
square H=3*3-----> 9 ft²
square J=3*3-----> 9 ft²
rectangle 1=3*4---> 12 ft²
square D=4*4-----> 16 ft²
square B=3*3-----> 9 ft²
square A=5*5-----> 25 ft²
square F=6*6-----> 36 ft²

the area total of rectangle is 12*11-------> 132 ft²

the answer is
the area of the given rectangle.is 132 ft²