Class 6 NCERT bridge course Answers Activity W2.5: Area – Same Area, Different Shapes

 

Activity W2.5: Area – Same Area, Different Shapes

● Take 10 pieces of dimension 1 x 1 unit. 

● Look at some of the following arrangements

• Do you find that all these arrangements occupy the same space, that is, they have the same area? 
•  Make some more arrangements of squares in different ways. 
•  What do you conclude?

Activity W2.5: Area – Same Area, Different Shapes

Objective:

To help students understand that area depends on the number of unit squares used, not the shape or arrangement. By arranging the same number of 1×1 unit squares in different ways, students see that the area remains constant.

Materials Needed:

• 10 square tiles or paper cutouts of size 1 unit × 1 unit

• Plain paper or grid paper

• Scissors and glue (optional)

• Pencil/pen for drawing shapes

Procedure:

1. Take 10 square pieces of 1×1 unit.

2. Arrange them in different shapes (straight line, L-shape, rectangle, zig-zag, etc.).

3. Draw or trace the shapes on paper to compare.

4. Observe and answer:

   • Do all the shapes cover the same area?

   • How do they look different?

Suggested Arrangements (Examples):

Shape	Description	Area
🔲🔲🔲🔲🔲🔲🔲🔲🔲🔲	1 row of 10 tiles (10 × 1 rectangle)	10 square units
🔲🔲🔲🔲🔲 🔲🔲🔲🔲🔲	2 rows of 5 tiles each (5 × 2 rectangle)	10 square units
🔲 🔲 🔲 🔲 🔲 🔲 🔲 🔲 🔲 🔲	1 column of 10 tiles (1 × 10 rectangle)	10 square units
🔲🔲🔲 🔲🔲🔲 🔲🔲🔲 🔲	L-shaped with pieces stacked	10 square units
Custom or irregular shape using all 10 tiles	Various	10 square units

Discussion Questions:

1. Do you find that all these arrangements occupy the same space, that is, they have the same area? 

            Yes. All arrangements use 10 unit squares, so they cover 10 square units, regardless of shape.

1. Make some more arrangements of squares in different ways. 

1. Do they look the same?
    No. The shapes look very different, even though the area is the same.

2. What do you conclude? What does this tell you about area?
   Area depends on the number of square units used, not how they are arranged.

3. Can different shapes have the same area?
   Yes! That's the key insight.

Conclusion:

This activity shows that different shapes can have the same area if they are made from the same number of unit squares. Area is a measure of how many square units cover a surface, not the shape or orientation of the figure.

Encourage students to explore:

• Creative patterns

• Symmetry

• New composite shapes
  All with the same total area!