Question

1. 4 in. 8 in. 8 in. 7 in. 1 in.

Explanation:

Step1: Find the missing side lengths

The vertical side of the upper - left rectangle: \(8 - 7=1\) in.
The horizontal side of the lower - left rectangle: \(4 + 8-(4 + 8 - 1)=1\) in.

Step2: Calculate the area of each rectangle

The area formula for a rectangle is \(A = l\times w\).
For the upper - left rectangle with \(l = 4\) in and \(w = 1\) in, \(A_1=4\times1 = 4\) \(in^2\).
For the middle rectangle with \(l=(4 + 8)\) in and \(w = 7\) in, \(A_2=(4 + 8)\times7=84\) \(in^2\).
For the lower - left rectangle with \(l = 1\) in and \(w = 1\) in, \(A_3=1\times1 = 1\) \(in^2\).

Step3: Sum up the areas of all rectangles

\(A=A_1+A_2+A_3=4 + 84+1\)

Answer:

\(89\) \(in^2\)