A square of side 8 cm has a smaller square of side 3 cm cut out from one corner. Sketch the resulting shape and find the area of the remaining figure.

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Step-by-Step Solution

Step 1: Identify the dimensions of the squares

We are given the side lengths of both the larger square and the smaller square that is cut out. Let's denote the side of the larger square as $S$ and the side of the smaller square as $s$ .

Step 2: Calculate the area of the larger square

The area of a square is calculated by squaring its side length. For the larger square, with side $S = 8 \text{ cm}$ , its area is $S^2 = (8 \text{ cm})^2 = 64 \text{ cm}^2$ .

Step 3: Calculate the area of the smaller square

Similarly, we calculate the area of the smaller square using its side length $s = 3 \text{ cm}$ . Its area is $s^2 = (3 \text{ cm})^2 = 9 \text{ cm}^2$ .

Step 4: Find the area of the remaining figure

To find the area of the remaining figure, we subtract the area of the smaller square (which was cut out) from the area of the larger square. This gives us $64 \text{ cm}^2 - 9 \text{ cm}^2 = 55 \text{ cm}^2$ .