Introduction to the Problem

In this article, we will solve a geometric problem related to the area calculation of a rectangular cardboard. We will start by understanding the dimensions of the original cardboard and the area of the square pieces that are to be cut out. By following a step-by-step approach, we will calculate the remaining area after the cuts have been made.

Step-by-Step Solution

1. Calculate the Area of the Original Rectangular Cardboard

The dimensions of the original rectangular cardboard are given as 6.5 meters long and 4.5 meters broad. To find the area, we use the formula for the area of a rectangle:

Areaoriginal length × breadth

Areaoriginal 6.5 m × 4.5 m 29.25 m2

Note: Since the final answer is expected in meters, we will keep the dimensions in meters throughout the calculations.

2. Convert the Dimensions of the Square Pieces to Meters

The dimensions of each square piece are given as 35 cm × 35 cm. To convert these dimensions into meters, we use the conversion factor that 1 meter equals 100 centimeters:

35 cm 0.35 m

3. Calculate the Area of One Square Piece

The area of a square can be calculated using the formula:

Areapiece side × side

Areapiece 0.35 m × 0.35 m 0.1225 m2

4. Calculate the Total Area of the 8 Square Pieces

Since we have 8 such square pieces, we need to multiply the area of one piece by 8:

Total Areacut 8 × 0.1225 m2 0.98 m2

5. Calculate the Area of the Remaining Portion of the Cardboard

The area of the remaining portion of the cardboard is the original area minus the total area of the 8 square pieces cut out:

Arearemaining Areaoriginal - Total Areacut

Arearemaining 29.25 m2 - 0.98 m2 28.27 m2

Answer

Thus, the area of the remaining portion of the cardboard is 28.27 m2.

Alternative Case: Area vs Side Length of Square Pieces

As an ambiguity or doubt created by Mr. , we consider two different interpretations of the problem:

Case 1: Area of Square Pieces is 35 sq cm

In this case, if '35 cm square' is treated as an area of a piece being 35 sq cm, then the total area of 8 such pieces is 35 x 8 sq cm 280 sq cm. Converting to square meters:

Total Areacut 0.0280 sq m

The area of the rectangular cardboard is 6.5 m × 4.5 m 29.25 sq m. Therefore, the remaining portion of the cupboard will be:

Arearemaining 29.25 - 0.0280 29.222 sq m

Case 2: Side Length of Square Pieces is 35 cm

If '35 cm square' is treated as a square piece of 35 cm side, the total area of 8 such pieces is 8 x 35 x 35 9800 sq cm. Converting to square meters:

Total Areacut 0.98 sq m

The area of the rectangular cardboard is 6.5 m × 4.5 m 29.25 sq m. Therefore, the remaining portion of the cupboard will be:

Arearemaining 29.25 - 0.98 28.27 sq m

Conclusion

From the above calculations, we see that the remaining area can vary depending on the interpretation of the '35 cm square'. Whether it is considered as an area of 35 sq cm or as a square piece with a side of 35 cm, the remaining area will be different. The commonly considered interpretation is the side length, resulting in a remaining area of 28.27 m2.