the area of the shaded part of the figure below can be determined in different ways. use the drop - down…

Explanation:

Step1: Area of the large square

The area of a square is (A = s^2), where (s) is the side - length. For the large square with (s = 5) in, (A_{large}=5\times5=25) square inches.

Step2: Area of the small square

For the small square with (s = 2) in, (A_{small}=2\times2 = 4) square inches.

Step3: Area of the shaded region (using the difference of squares)

The area of the shaded region (A=A_{large}-A_{small}). So (A = 25-4=21) square inches.

Step4: Decomposition into rectangles

The figure can be decomposed into (4) rectangles.

Step5: Decomposition into trapezoids

If decomposed into (4) trapezoids, the height of each trapezoid (h=\frac{5 - 2}{2}=1.5) in. The non - 5 in base of the trapezoid: Let's consider the trapezoid formula (A=\frac{(b_1 + b_2)h}{2}). Another way to find the base: If we assume the trapezoid, using the fact that the inner square has side - length (2) in. The non - 5 in base (b = 2) in. Using the trapezoid formula for (4) trapezoids: (A = 4\times\frac{(2 + 5)\times1.5}{2}=4\times\frac{7\times1.5}{2}=4\times5.25 = 21) square inches

Answer:

The figure can be decomposed into (4) rectangles, or the figure can be decomposed into (4) trapezoids with heights of (1.5) in. and bases of (2) in. and (5) in. Using either method, the total area of the shaded figure is (21) square inches.