Question

all of the quadrilaterals in the shape below are squares. find the area of the shaded region.

Explanation:

Step1: Find side - length of large square

The side - length of the large square is the sum of the side - length of the small square and the side - length of the medium square. Given the side - length of the small square is 2 and the side - length of the medium square is 8, so the side - length of the large square is \(2 + 8=10\).

Step2: Calculate area of large square

The area formula for a square is \(A = s^2\), where \(s\) is the side - length. For the large square with \(s = 10\), its area \(A_{large}=10^2 = 100\).

Step3: Calculate area of medium square

For the medium square with side - length \(s = 8\), its area \(A_{medium}=8^2=64\).

Step4: Calculate area of small square

For the small square with side - length \(s = 2\), its area \(A_{small}=2^2 = 4\).

Step5: Calculate area of shaded region

The area of the shaded region is the area of the large square minus the area of the medium square and the area of the small square. \(A_{shaded}=A_{large}-A_{medium}-A_{small}=100 - 64-4=32\).

Answer:

32