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Figures with same perimeter have different area Video Lecture - Class 5
FAQs on Figures with same perimeter have different area Video Lecture - Class 5
| 1. What does it mean when figures have the same perimeter but different areas? |  |
Ans. When figures have the same perimeter, it means that the total length of their boundaries is equal. However, if their areas are different, it implies that the space covered inside the figures is not the same. In other words, even though the lengths of their boundaries are equal, the distribution of that length is different, resulting in different areas.
| 2. How can figures with the same perimeter have different areas? | |
Ans. Figures with the same perimeter can have different areas because the shape and arrangement of their sides can vary. For example, two rectangles can have the same perimeter, but if one is a square and the other is a long and narrow rectangle, their areas will be different. The square will cover more space within its boundaries compared to the long and narrow rectangle.
| 3. Can you provide an example to understand figures with the same perimeter but different areas? | |
Ans. Certainly! Let's take two rectangles as an example. Consider one rectangle with sides measuring 4 units and 6 units and another rectangle with sides measuring 5 units and 5 units. Both rectangles have the same perimeter of 20 units (4+6+4+6 = 20 and 5+5+5+5 = 20). However, the area of the first rectangle is 24 square units (4 x 6 = 24), while the area of the second rectangle is 25 square units (5 x 5 = 25). Despite having the same perimeter, the two rectangles differ in their areas.
| 4. Why is it possible for figures with different shapes to have the same perimeter? | |
Ans. Figures with different shapes can have the same perimeter because the distribution of lengths along their boundaries can compensate for variations in shape. Different combinations of side lengths can add up to the same total, resulting in the same perimeter. For example, a square and a rectangle can have the same perimeter if the lengths of their sides are appropriately chosen.
| 5. How does the concept of figures with the same perimeter but different areas relate to real-life situations? | |
Ans. The concept of figures with the same perimeter but different areas is applicable to various real-life situations. For instance, it can be observed in gardening, where rectangular flower beds with different proportions can have the same perimeter but different areas. Similarly, in construction, different room layouts with the same total wall length can have different floor areas. This concept is also significant in optimizing the use of materials, as it highlights how changing the shape of a figure can affect its covered area while maintaining the same amount of material for its boundary.
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Nov 16, 2024 Last updated |
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