A square with a side of 5 cm was cut along the dotted lines as shown in the figure. This created a square piece of side 3 cm. The centres of the two squares are the same. What is the area (in cm²) of the shaded portion?
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When calculating the shaded area after removing a smaller square from a larger square, simply subtract the area of the smaller square from the area of the larger square.
Step 1: Understanding the problem. We are given a large square with a side of 5 cm, and a smaller square with a side of 3 cm. The centers of both squares are the same, and the smaller square is cut from the larger one. The shaded portion is the area left after the smaller square is cut out from the larger square. Step 2: Calculating the area of the larger square. The area of a square is given by the formula: \[ \text{Area of the larger square} = \text{side}^2 = 5^2 = 25 \, \text{cm}^2 \] Step 3: Calculating the area of the smaller square. Similarly, the area of the smaller square is: \[ \text{Area of the smaller square} = \text{side}^2 = 3^2 = 9 \, \text{cm}^2 \] Step 4: Finding the shaded area. The shaded area is the area of the larger square minus the area of the smaller square: \[ \text{Shaded area} = 25 - 9 = 16 \, \text{cm}^2 \] \[ \boxed{16 \, \text{cm}^2} \]
