Question

click the arrows to choose an answer from each menu.
the figure can be decomposed into choose... rectangles,
or the figure can be decomposed into 4 trapezoids with heights of choose... in. and in. and 5 in.
bases of choose... in. and 5 in.
using either method, the total area of the shaded figure is choose... square inches.

Explanation:

Step1: Identify figure dimensions

The outer shape is a square with side length $5$ in, and the inner unshaped square has side length $2$ in.

Step2: Calculate area of outer square

Area of square: $A_{outer} = s^2 = 5^2 = 25$ square inches

Step3: Calculate area of inner square

Area of square: $A_{inner} = s^2 = 2^2 = 4$ square inches

Step4: Find shaded area (subtract areas)

Shaded area = $A_{outer} - A_{inner} = 25 - 4$

Answer:

The figure can be decomposed into 2 rectangles and 2 squares (or alternatively, the figure can be decomposed into 4 trapezoids with heights of $\frac{3}{2}$ in and bases of 2 in and 5 in).
The total area of the shaded figure is $\boldsymbol{21}$ square inches.